View source for User:RazrRekr201/Table of constants

== Table of constants and other irrational or transcendental numbers  ==


{| class="wikitable sortable"
|-
!  Value  ||    Name    ||Graphics||Symbol|| LaTeX ||    Formula    ||Nº|| OEIS || Continued fraction||Year||Web format
|-

<!--------------------------------------v---------------------------------------------->
|0,70444 22009 99165 59273 
||Carefree constant <sub>2</sub> <ref>{{cite book 
|author= Steven Finch
|title= Unitarism and Infinitarism
|url= http://www.people.fas.harvard.edu/~sfinch/csolve/try.pdf
|year= 2004
|editor= Harvard.edu
|page= 1
}}</ref>
|<br><br><br><br>
|bgcolor=#e0f0f0 align=center|<math>\mathcal{C}_2</math>
||<math> \underset{ p_n: \, {prime}}{\prod_{n = 1}^\infty \left(1 - \frac{1}{p_n(p_n+1)}\right)} </math>
||N[prod[n=1 to ∞] <br> {1 - 1/(prime(n)* <br> (prime(n)+1))}]
||
||{{OEIS2C|A065463}}
||[0;1,2,2,1,1,1,1,4,2,1,1,3,703,2,1,1,1,3,5,1,...]
||
||<small> 0.70444220099916559273660335032663721 </small>
|-

<!--------------------------------------- v ------------------------------------------->
|1.84775 90650 22573 51225 <ref group=Mw>{{MathWorld|Self-AvoidingWalkConnectiveConstant|Self-Avoiding Walk Connective Constant}}</ref>
||[[Connective constant]] <ref>{{cite book 
|author= Mireille Bousquet-Mélou
|title= Two-dimensional self-avoiding walks
|url= http://www.labri.fr/perso/bousquet/Exposes/fpsac-saw.pdf
|editor= CNRS, LaBRI, Bordeaux, France
}}</ref><ref>{{cite book 
|author= Hugo Duminil-Copin and Stanislav Smirnov
|title= The connective constant of the honeycomb lattice √ (2 + √ 2)
|url= http://www.unige.ch/~smirnov/slides/slides-saw.pdf
|year= 2011
|editor= Universite de Geneve.
}}</ref>
|bgcolor=#ffffff align=center|[[Image:HEX-LATTICE-20.gif|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\mu}</math>
||<math>\sqrt{2 + \sqrt{2}} \; = \lim_{n \rightarrow \infty} c_n^{1/n} </math>
as a root of the polynomial <math>: \; x ^ 4-4 x ^ 2 + 2=0</math>
||sqrt(2+sqrt(2))
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||{{OEIS2C|A179260}}
||[1;1,5,1,1,3,6,1,3,3,10,10,1,1,1,5,2,3,1,1,3,...]
||
||<small> 1.84775906502257351225636637879357657 </small>
|-

<!------------------------------------------v------------------------------------------>
|0.30366 30028 98732 65859 <ref group=Mw>{{MathWorld|Gauss-Kuzmin-WirsingConstant|Gauss-Kuzmin-Wirsing Constant}}</ref>
||Gauss-Kuzmin-Wirsing constant <ref>{{cite book
|author= W.A. Coppel
|title= Number Theory: An Introduction to Mathematics
|page= 480
|year= 2000
|editor= Springer
|isbn= 978-0-387-89485-0
|url= http://books.google.com/books?id=We5FAAAAQBAJ&lpg=PA480&dq=0.303663&hl=es&pg=PA480#v=onepage&q=0.303663&f=false
}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{\lambda}_{2}</math>
||<math>\lim_{n \to \infty}\frac{F_n(x) - \ln(1 - x)}{(-\lambda)^n} = \Psi(x),</math>
where <math>\Psi(x)</math> is an analytic function with <math>\Psi(0) \!=\! \Psi(1) \!=\! 0</math>.
||
||
||{{OEIS2C|A038517}}
||[0;3,3,2,2,3,13,1,174,1,1,1,2,2,2,1,1,1,2,2,1,...]
||1973
||<small> 0.30366300289873265859744812190155623 </small>
|-

<!------------------------------------------v----------------------------------------->
|1,57079 63267 94896 61923 <ref group=Mw>{{MathWorld|WallisFormula|Wallis Formula}}</ref>
||Favard constant K1 <br> [[Wallis product]] <ref>{{cite book 
|author= James Stuart Tanton
|title= Encyclopedia of Mathematics
|url= http://books.google.com/books?id=MfKKMSuthacC&pg=PA529&dq=wallis+product&hl=es&sa=X&ei=1OsYU-X4O8PnywPuz4CoBg&redir_esc=y#v=onepage&q=wallis%20product&f=false
|year= 2005
|publisher= 
|isbn=9781438110080
|page= 529
}}</ref>
||[[Image:Wallis product-chart.png|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\frac{\pi}{2}}</math>
||<math> \prod_{n=1}^{\infty} \left(\frac{4n^2}{4n^2 - 1}\right) = \frac{2}{1} \cdot \frac{2}{3} \cdot \frac{4}{3} \cdot \frac{4}{5} \cdot \frac{6}{5} \cdot \frac{6}{7} \cdot \frac{8}{7} \cdot \frac{8}{9} \cdots </math>
||Prod[n=1 to ∞] <br> {(4n^2)/(4n^2-1)}
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A069196}}
||[1;1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,1,5,1...]
||1655
||<small> 1.57079632679489661923132169163975144 </small>
|-

<!------------------------------------------v----------------------------------------->
|1,60669 51524 15291 76378 <ref group=Mw>{{MathWorld|Erdos-BorweinConstant|Erdos-Borwein Constant}}</ref>
||[[Erdős–Borwein constant]]<ref>{{cite book 
|author= Robert Baillie
|title= Summing The Curious Series of Kempner and Irwin
|url= http://arxiv.org/pdf/0806.4410.pdf
|year= 2013 
|editor= arxiv
|isbn= 
|page= 9
}}</ref><ref>{{cite book 
|author= Leonhard Euler
|title= Consideratio quarumdam serierum, quae singularibus proprietatibus sunt praeditae
|url= http://www.math.dartmouth.edu/~euler/pages/E190.html
|year= 1749
|page= 108 
}}</ref>
||<br><br><br>
| bgcolor=#e0f0f0 align=center|<math>{E}_{\,B}</math>
||<math>\sum_{m=1}^{\infty} \sum_{n=1}^{\infty}\frac{1}{2^{mn}} =\sum_{n=1}^{\infty}\frac{1}{2^n-1} = \frac{1}{1} \! + \! \frac{1}{3} \! + \! \frac{1}{7} \! + \! \frac{1}{15} \! + \! ...</math>
||sum[n=1 to ∞]<br>{1/(2^n-1)}
|style="text-align:center;"|'''''[[Irrational number|I]]'''''
||{{OEIS2C|A065442}}
||[1;1,1,1,1,5,2,1,2,29,4,1,2,2,2,2,6,1,7,1,...]
||1949 
||<small> 1.60669515241529176378330152319092458 </small>
|-

<!----------------------------------------------v------------------------------------------->
|1.61803 39887 49894 84820 <ref group=Mw>{{MathWorld|GoldenRatio|Golden Ratio}}</ref>
||Phi, [[Golden ratio]] <ref>{{cite book 
|author= Timothy Gowers, June Barrow-Green, Imre Leade
|title= The Princeton Companion to Mathematics
|url=https://books.google.es/books?id=ZOfUsvemJDMC&lpg=PA316&dq=1.618033988749894848&hl=es&pg=PA316#v=onepage&q=1.618033988749894848&f=false
|year= 2007
|editor= Princeton University Press
|isbn= 978-0-691-11880-2 
|page= 316
}}</ref>
||[[Image:Animation GoldenerSchnitt.gif|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\varphi}</math>
|| <math>\frac{1 + \sqrt{5}}{2} = \sqrt{1 + \sqrt{1 + \sqrt{1 + \sqrt{1 + \cdots}}}} </math>
||(1+5^(1/2))/2
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||{{OEIS2C|A001622}}
||[0;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...]<br> = [0;{{overline|1}},...]
||-300 ~
||<small> 1.61803398874989484820458633436563812 </small>
|-

<!-----------------------------------------v---------------------------------------------->
|1.64493 40668 48226 43647 <ref group=Mw>{{MathWorld|RiemannZetaFunctionZeta2|Riemann Zeta Function Zeta 2}}</ref>
||Riemann Function Zeta(2)
||
| bgcolor=#e0f0f0 align=center|<math>{\zeta}(\,2)</math>
||<math> \frac{\pi^2}{6} = \sum_{n=1}^\infty\frac{1}{n^2} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots</math>
||Sum[n=1 to ∞]<br>{1/n^2}
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A013661}}
||[1;1,1,1,4,2,4,7,1,4,2,3,4,10 1,2,1,1,1,15,...]
||1826 <br> to <br> 1866
||<small> 1.64493406684822643647241516664602519 </small>
|-

<!----------------------------------------------v------------------------------------------->
|1.73205 08075 68877 29352 <ref group=Mw>{{MathWorld|TheodorussConstant|Theodorus's Constant}}</ref>
||[[Theodorus constant]]<ref>{{cite book 
|author= Vijaya AV
|title= Figuring Out Mathematics
|url= http://books.google.com/books?id=xAwukpHCqH0C&pg=PA15&dq=1.732050807&hl=es&sa=X&ei=FyQCU470K4a7ygOrw4HgBA&redir_esc=y#v=onepage&q=1.732050807&f=false
|year= 2007
|editor= Dorling Kindcrsley (India) Pvt. Lid.
|isbn= 978-81-317-0359-5 
|page= 15
}}</ref>
||[[Image:Square root of 3 in cube.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math>\sqrt{3} </math>
||<math> \sqrt[3]{3 \,\sqrt[3]{3 \, \sqrt[3]{3 \,\sqrt[3]{3 \,\sqrt[3]{3  \,\cdots}}}}} </math>
||(3(3(3(3(3(3(3) <br> ^1/3)^1/3)^1/3) <br> ^1/3)^1/3)^1/3) <br> ^1/3 ...
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||{{OEIS2C|A002194}}
||[1;1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,...] <br> = [1;{{overline|1,2}},...]
||-465 <br> to <br> -398
||<small> 1.73205080756887729352744634150587237 </small>
|-

<!---------------------------------------------v---------------------------------------------->
|1.75793 27566 18004 53270 <ref group=Mw>{{MathWorld|NestedRadicalConstant|Nested Radical Constant}}</ref>
||Kasner number
||
| bgcolor=#e0f0f0 align=center|<math>{R}</math>
||<math>\sqrt{1 + \sqrt{2 + \sqrt{3 + \sqrt{4 + \cdots}}}} </math>
|| Fold[Sqrt[#1+#2]<br> &,0,Reverse <br> [Range[20]]]
||
||{{OEIS2C|A072449}}
||[1;1,3,7,1,1,1,2,3,1,4,1,1,2,1,2,20,1,2,2,...]
||1878 <br> a <br> 1955
||<small> 1.75793275661800453270881963821813852 </small>
|-

<!--------------------------------------------v------------------------------------------>
|2.29558 71493 92638 07403 <ref group=Mw>{{MathWorld|UniversalParabolicConstant|Universal Parabolic Constant}}</ref>
||[[Universal parabolic constant]] <ref>{{cite book
|author= Steven Finch
|title= Errata and Addenda to Mathematical Constants
|page= 59
|year= 2014
|editor= Harvard.edu
|isbn= 
|url= http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf
}}</ref>
||[[Image:Parabola animada.gif|100px]]
| bgcolor=#e0f0f0 align=center|<math> {P}_{\,2} </math>
||<math>\ln(1 + \sqrt2) + \sqrt2 \; = \; \operatorname{arcsinh}(1)+\sqrt{2}</math>
||ln(1+sqrt 2)+sqrt 2
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A103710}}
||[2;3,2,1,1,1,1,3,3,1,1,4,2,3,2,7,1,6,1,8,7,2,1,...]
||
||<small> 2.29558714939263807403429804918949038 </small>
|-

<!------------------------------------------v-------------------------------------------->
|1.78657 64593 65922 46345 <ref group=Mw>{{MathWorld|SilvermanConstant|Silverman Constant}}</ref>
||Silverman constant<ref>{{cite book 
|author= Steven Finch
|title= Series involving Arithmetric Functions
|url= http://www.people.fas.harvard.edu/~sfinch/csolve/arth.pdf
|year= 2007
|editor= Harvard.edu
|page= 1
}}</ref>
||<br><br><br><br>
|bgcolor=#e0f0f0 align=center|<math>{\mathcal{S}_{_{m}}}</math>
||<math> \sum_{n = 1}^\infty  \frac {1}{\phi (n)\sigma_1(n)}   = \underset{ p_n: \, {prime}}{ \prod_{n = 1}^\infty \left( 1 + \sum_{k = 1}^\infty  \frac {1}{p_n^{2k} - p_n^{k-1}}\right)}</math> <br> <center> ø() = [[Euler's totient function]], σ<sub>1</sub>() = [[Divisor function]].</center>
||Sum[n=1 to ∞] <br> {1/[EulerPhi(n) <br> <small>DivisorSigma</small>(1,n)]}
||
||{{OEIS2C|A093827}}  
||[1;1,3,1,2,5,1,65,11,2,1,2,13,1,4,1,1,1,2,5,4,...]
||
||<small> 1.78657645936592246345859047554131575 </small>
|-

<!--------------------------------------------v------------------------------------------->
|2.59807 62113 53315 94029 <ref group=Mw>{{MathWorld|Twenty-VertexEntropyConstant|Twenty-Vertex Entropy Constant}}</ref>
||Area of the regular hexagon with side equal to 1 <ref>{{cite book 
|author= Nayar
|title= The Steel Handbook
|url= http://books.google.com/books?id=3QomboYUpVEC&lpg=PA953&dq=2.598076&hl=es&pg=PA953#v=onepage&q=2.598076&f=false
|year= 
|editor= Tata McGraw-Hill Education. 
|page= 953
}}</ref>
|bgcolor=#ffffff align=center|[[Image:Esagono.png|80px]]
 |bgcolor=#e0f0f0 align=center|<math>\mathcal{A}_6</math>
||<math> \frac{3 \sqrt{3}}{2}\,l^2 </math>
||3 sqrt(3)/2
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||{{OEIS2C|A104956}}
||[2;1,1,2,20,2,1,1,4,1,1,2,20,2,1,1,4,1,1,2,20,...] <br> [2;{{overline|1,1,2,20,2,1,1,4}}]
||
||<small> 2.59807621135331594029116951225880855 </small>
|-

<!----------------------------------------v-------------------------------------------->
|0.66131 70494 69622 33528 <ref group=Mw>{{MathWorld|Feller-TornierConstant|Feller-Tornier Constant}}</ref>
||Feller-Tornier <br> constant <ref>{{cite book 
|author= ECKFORD COHEN
|title= SOME ASYMPTOTIC FORMULAS IN THE THEORY OF NUMBERS
|url= http://www.ams.org/journals/tran/1964-112-02/S0002-9947-1964-0166181-5/S0002-9947-1964-0166181-5.pdf
|year= 1962
|editor= University of Tennessee
|page= 220
}}</ref>
||<br><br><br><br>
|bgcolor=#e0f0f0 align=center|<math>{\mathcal{C}_{_{FT}}}</math>
||<math>\underset{p_n: \, {prime}}{\frac{1}{2}\prod_{n = 1}^\infty \left(1-\frac{2}{p_n^2}\right){+}\frac{1}{2}} =\frac{3}{\pi^2}\prod_{n = 1}^\infty \left(1-\frac{1}{p_n^2-1}\right){+}\frac{1}{2}</math>
||[prod[n=1 to ∞] <br> {1-2/prime(n)^2}] <br> /2 + 1/2
|style="text-align:center;"|'''''[[Transcendental number|T]]''''' ?
||{{OEIS2C|A065493}}  
||[0;1,1,1,20,9,1,2,5,1,2,3,2,3,38,8,1,16,2,2,...]
||1932
||<small> 0.66131704946962233528976584627411853 </small>
|-

<!-----------------------------------------v--------------------------------------------->
|1.46099 84862 06318 35815 <ref group=Mw>{{MathWorld|BaxtersFour-ColoringConstant|Baxter's Four-Coloring Constant}}</ref>
||Baxter's <br> Four-coloring <br> constant <ref>{{cite book 
|author= Paul B. Slater
|title= A Hypergeometric Formula ...
|url= http://arxiv.org/pdf/1203.4498.pdf
|year= 2013
|editor= University of California
|page= 9
}}</ref>
|bgcolor=#ffffff align=center| Mapamundi [[Image:Four color world map.svg|100px]] Four-Coloring
 |bgcolor=#e0f0f0 align=center|<math>\mathcal{C}^2</math>
||<math> \prod_{n = 1}^\infty \frac{(3n-1)^2}{(3n-2)(3n)}  = \frac {3}{4\pi^2} \,\Gamma \left(\frac {1}{3}\right)^3 </math>
<center> Γ() = [[Gamma function]] </center>
||3×Gamma(1/3) <br> ^3/(4 pi^2)
||
||{{OEIS2C|A224273}}
||[1;2,5,1,10,8,1,12,3,1,5,3,5,8,2,1,23,1,2,161,...]
||1970
||<small> 1.46099848620631835815887311784605969 </small>
|-

<!-------------------------------------------v-------------------------------------------->
|1.92756 19754 82925 30426 <ref group=Mw>{{MathWorld|TetranacciConstant|Tetranacci Constant}}</ref>
||[[Generalizations of Fibonacci numbers#Tetranacci numbers|Tetranacci constant]]
<!---
<ref>{{cite book 
|author= 
|title= 
|url= 
|year= 
|editor= 
|page= 
}}</ref>
--->
||<br><br>
|bgcolor=#e0f0f0 align=center|<math>\mathcal{T}</math>
||Positive root of <math>: \;\; x^4-x^3-x^2-x-1=0</math>
||Root[x+x^-4-2=0]
||
||{{OEIS2C|A086088}}
||[1;1,12,1,4,7,1,21,1,2,1,4,6,1,10,1,2,2,1,7,1,...]
||
||<small> 1.92756197548292530426190586173662216 </small>
|-

<!----------------------------------------------v---------------------------------------------->
|1.00743 47568 84279 37609 <ref group=Mw>{{MathWorld|PrinceRupertsCube|Prince Rupert's Cube}}</ref>
||[[:en:Prince Rupert's cube#Generalizations|DeVicci's tesseract constant]]
<!---
<ref>{{cite book 
|author= 
|title= 
|url= 
|year= 
|editor= 
|page= 
}}</ref>
--->
||[[Image:8-cell-orig.gif|100px]]
|bgcolor=#e0f0f0 align=center|<math>{f_{(3,4)}}</math>
||The largest cube that can pass through in an 4D hypercube.
Positive root of <math>: \;\; 4x^4{-}28x^3{-}7x^2{+}16x{+}16=0</math>
||Root[4*x^8-28*x^6 <br> -7*x^4+16*x^2+16 <br> =0]
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||{{OEIS2C|A243309}}
||[1;134,1,1,73,3,1,5,2,1,6,3,11,4,1,5,5,1,1,48,...]
||
||<small> 1.00743475688427937609825359523109914 </small>
|-

<!----------------------------------------------v------------------------------------------->
|1.70521 11401 05367 76428 <ref group=Mw>{{MathWorld|NivensConstant|Niven's Constant}}</ref>
||[[Niven's constant]] <ref>{{cite book
|author= Ivan Niven 
|title= Averages of exponents in factoring integers
|url= http://www.ams.org/journals/proc/1969-022-02/S0002-9939-1969-0241373-5/S0002-9939-1969-0241373-5.pdf
}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{C}</math>
||<math>1+\sum_{n = 2}^\infty \left(1-\frac{1}{\zeta(n)} \right)</math>
||1+ Sum[n=2 to ∞]<br>{1-(1/Zeta(n))}
||
||{{OEIS2C|A033150}}
||[1;1,2,2,1,1,4,1,1,3,4,4,8,4,1,1,2,1,1,11,1,...]
||1969
||<small> 1.70521114010536776428855145343450816 </small>
|-

<!---------------------------------------------v------------------------------------------>
|0.60459 97880 78072 61686 <ref group=Mw>{{MathWorld|CentralBinomialCoefficient|Central Binomial Coefficient}}</ref>
||Relationship among the area of an equilateral triangle and the inscribed circle.
||[[Image:Fano plane.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math> \frac{\pi}{3 \sqrt 3}</math>
||<br><math> \sum_{n = 1}^\infty \frac{1}{n{2n \choose n}} =  1 - \frac{1}{2} + \frac{1}{4} - \frac{1}{5} + \frac{1}{7} - \frac{1}{8} + \cdots</math>  <center> [[Dirichlet series]] </center>
||Sum[1/(n <br>Binomial[2 n, n])<br>, {n, 1, ∞}]
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A073010}}
||[0;1,1,1,1,8,10,2,2,3,3,1,9,2,5,4,1,27,27,6,6,...]
||
||<small> 0.60459978807807261686469275254738524 </small>
|-

<!--------------------------------------------v------------------------------------------->
|1.15470 05383 79251 52901 <ref group=Mw>{{MathWorld|HermiteConstants|Hermite Constants}}</ref>
|| [[:fr:Constante d'Hermite|Hermite Constant]] <ref>{{cite book
|author= Steven Finch
|title= Errata and Addenda to Mathematical Constants
|page=
|year= 2014
|editor= Harvard.edu
|isbn= 
|url= http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf
}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math> \gamma_{_{2}} </math>
||<math> \frac{2}{\sqrt{3}} = \frac{1}{\cos \, (\frac{\pi}{6})} </math>
||2/sqrt(3)
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||1+<br>{{OEIS2C|A246724}}
||[1;6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,...] <br>  [1;{{overline|6,2}}]
|| 
||<small> 1.15470053837925152901829756100391491 </small>
|-

<!---------------------------------------------v----------------------------------------->
|0.41245 40336 40107 59778  <ref group=Mw>{{MathWorld|Thue-MorseConstant|Thue-Morse Constant}}</ref>
||[[Prouhet–Thue–Morse constant]] <ref>{{cite book
|author= Steven Finch
|title= Errata and Addenda to Mathematical Constants
|page= 53
|year= 2014
|editor= Harvard.edu
|isbn= 
|url= http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf
}}</ref>
||[[Image:Thue-MorseRecurrence.gif|100px]]
| bgcolor=#e0f0f0 align=center|<math> \tau </math>
||<math> \sum_{n=0}^{\infty} \frac{t_n}{2^{n+1}} </math>   &nbsp;&nbsp; where <math> {t_n} </math>  is the [[Thue–Morse sequence]]  &nbsp;and <br> Where <math> \tau(x) = \sum_{n=0}^{\infty} (-1)^{t_n} \, x^n  = \prod_{n=0}^{\infty} ( 1 - x^{2^n} )</math>
||
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A014571}}
||[0;2,2,2,1,4,3,5,2,1,4,2,1,5,44,1,4,1,2,4,1,1,...]
||
||<small> 0.41245403364010759778336136825845528 </small> 
|-

<!--------------------------------------------v---------------------------------------->
|0.58057 75582 04892 40229 <ref group=Mw>{{MathWorld|PellConstant|Pell Constant}}</ref>
||Pell Constant <ref>{{cite book 
|author= FRANZ LEMMERMEYER
|title= HIGHER DESCENT ON PELL CONICS. I. FROM LEGENDRE TO SELMER
|url= http://arxiv.org/pdf/math/0311309.pdf
|year= 2003
|editor= arxiv.org
|page= 13
}}</ref>
||<br><br><br>
| bgcolor=#e0f0f0 align=center|<math>{\mathcal{P}_{_{Pell}}}</math>
||<math>1- \prod_{n = 0}^\infty \left(1-\frac{1}{2^{2n+1}}\right) </math>
||N[1-prod[n=0 to ∞] <br> {1-1/(2^(2n+1)}]
|style="text-align:center;"|'''''[[Transcendental number|T]]''''' ?
||{{OEIS2C|A141848}}
||[0;1,1,2,1,1,1,1,14,1,3,1,1,6,9,18,7,1,27,1,1,...]
||
||<small> 0.58057755820489240229004389229702574 </small>
|-

<!----------------------------------------------v-------------------------------------------->
|0.66274 34193 49181 58097 <ref group=Mw>{{MathWorld|LaplaceLimit|Laplace Limit}}</ref>
||[[Laplace limit]] <ref>{{cite book
|author= Howard Curtis
|title= [[Orbital Mechanics for Engineering Students]]
|page= 159
|year= 2014
|editor= Elsevier
|isbn= 978-0-08-097747-8
}}</ref>
||[[Image:Laplace limit.png|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\lambda}</math>
||<math> \frac{ x \; e^\sqrt{x^2+1}}{\sqrt{x^2+1}+1} = 1</math>
||(x e^sqrt(x^2+1))<br>/(sqrt(x^2+1)+1) <br> = 1
||
||{{OEIS2C|A033259}}
||[0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,1,1,2,1601,...]
||1782 ~
||<small> 0.66274341934918158097474209710925290 </small>
|-

<!-------------------------------------------v---------------------------------------------->
|0.17150 04931 41536 06586 <ref group=Mw>{{MathWorld|Hall-MontgomeryConstant|Hall-Montgomery Constant}}</ref>
||Hall-Montgomery Constant <ref>{{cite book
|author= Andrew Granville and K. Soundararajan
|title= The spectrum of multiplicative functions
|page= 3
|year= 1999
|editor= Arxiv
|isbn= 
|url= http://arxiv.org/pdf/math/9909190.pdf
}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math> {{\delta}_{_{0}}} </math>
|| <math> 1 + \frac{\pi^2}{6} +2 \; \mathrm{Li}_2 \left(-\sqrt{e}\;\right) 
\quad \mathrm{Li}_2 \, \scriptstyle \text{= Dilogarithm integral} </math>
||1 + Pi^2/6 + 2*PolyLog[2, -Sqrt[E]]
||
||{{OEIS2C|A143301}}
||[0;5,1,4,1,10,1,1,11,18,1,2,19,14,1,51,1,2,1,...]
||
||<small> 0.17150049314153606586043997155521210 </small> 
|-

<!----------------------------------------------v------------------------------------------->
|1.55138 75245 48320 39226 <ref group=Mw>{{MathWorld|CalabisTriangle|Calabi's Triangle}}</ref>
||[[Calabi triangle]] constant <ref>{{cite book
|author= John Horton Conway, Richard K. Guy
|title= The Book of Numbers
|page= 242
|year= 1995
|editor= Copernicus
|isbn= 0-387-97993-X
|url= http://books.google.com/books?id=0--3rcO7dMYC&lpg=PA206&dq=%22Calabi%20triangle%22&hl=es&pg=PA206#v=onepage&q=%22Calabi%20triangle%22&f=false
}}</ref>
||[[Image:Calabi triangle.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math> {C_{_{CR}}} </math>
|| <math> {1 \over 3} + {(-23 + 3i \sqrt{237})^{\tfrac13} \over 3 \cdot 2^{\tfrac23}} + {11 \over 3 (2 (-23 + 3i \sqrt{237}))^{\tfrac13}} </math>
||FindRoot[ <br> 2x^3-2x^2-3x+2 <br> ==0, {x, 1.5}, <br><small> WorkingPrecision->40]</small>
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||{{OEIS2C|A046095}}
||[1;1,1,4,2,1,2,1,5,2,1,3,1,1,390,1,1,2,11,6,2,...]
||1946 ~
||<small> 1.55138752454832039226195251026462381 </small> 
|-

<!------------------------------------------v--------------------------------------------->
|1.22541 67024 65177 64512 <ref group=Mw>{{MathWorld|GammaFunction|Gamma Function}}</ref>
||Gamma(3/4) <ref>{{cite book
|author= John Derbyshire
|title= Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
|page= 147
|year= 2003
|editor= Joseph Henry Press
|isbn= 0-309-08549-7
|url=http://books.google.com/books?id=qsoqLNQUIJMC&lpg=PA147&ots=pJnh9sLt02&dq=1.2254167024&hl=es&pg=PA147#v=onepage&q=1.2254167024&f=false
}}</ref>
||<br><br><br>
| bgcolor=#e0f0f0 align=center|<math>\Gamma(\tfrac34)</math>
||<math>\left(-1+\frac{3}{4}\right)! = \left(-\frac{1}{4}\right)!</math>
||(-1+3/4)!
||
||{{OEIS2C|A068465}}
||[1;4,2,3,2,2,1,1,1,2,1,4,7,1,171,3,2,3,1,1,8,3,...]
||
||<small> 1.22541670246517764512909830336289053 </small>
|-

<!------------------------------------------v---------------------------------------------->
|1.20205 69031 59594 28539 <ref group=Mw>{{MathWorld|AperysConstant|Apery's Constant}}</ref>
||[[Apéry's constant]] <ref>{{cite book 
|author= Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadelantl, William B. Jones.
|title= Handbook of Continued Fractions for Special Functions
|url= http://books.google.com/books?id=DQtpJaEs4NIC&lpg=PA188&ots=GiV4L5VymA&dq=1.202056903159594285399738&hl=es&pg=PA188#v=onepage&q=1.202056903159594285399738&f=false
|year= 2008
|publisher= Springer
|isbn= 978-1-4020-6948-2
|page= 188
}}</ref>
||[[Image:Apéry's constant.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math>\zeta(3)</math>
||<math>\sum_{n=1}^\infty\frac{1}{n^3} = \frac{1}{1^3}+\frac{1}{2^3} + \frac{1}{3^3} + \frac{1}{4^3} + \frac{1}{5^3} + \cdots= </math>
<math>\frac{1}{2} \sum_{n=1}^\infty \frac{H_n}{n^2} =
\frac{1}{2} \sum_{i=1}^\infty \sum_{j=1}^\infty \frac{1}{ij(i{+}j)}=
\!\!\int \limits_0^1 \!\!\int \limits_0^1 \!\!\int \limits_0^1 \frac{\mathrm{d}x \mathrm{d}y \mathrm{d}z}{1 - xyz} </math>
||Sum[n=1 to ∞]<br>{1/n^3}
|style="text-align:center;"|'''''[[Irrational number|I]]'''''
||{{OEIS2C|A010774}}
||[1;4,1,18,1,1,1,4,1,9,9,2,1,1,1,2,7,1,1,7,11,...]
||1979
||<small> 1.20205690315959428539973816151144999 </small>
|-

<!----------------------------------------------v--------------------------------------->
|0.91596 55941 77219 01505 <ref group=Mw>{{MathWorld|CatalansConstant|Catalan's Constant}}</ref>
||[[Catalan's constant]]<ref>{{cite book 
|author= Henri Cohen
|title= Number Theory: Volume II: Analytic and Modern Tools
|url=http://books.google.com/books?id=5Lp-tGZR25sC&pg=PA127&dq=0.91596559417721901505460351493238411&hl=es&sa=X&ei=s9UoU_ObB-WW0QWs6YDICQ&ved=0CDgQuwUwAA#v=onepage&q=0.91596559417721901505460351493238411&f=false 
|year= 2000
|publisher= Springer
|isbn= 978-0-387-49893-5
|page= 127
}}</ref><ref>{{cite book 
|author= H. M. Srivastava,Choi Junesang
|title= Series Associated With the Zeta and Related Functions
|url= http://books.google.com/books?id=NBcSzUlaWWAC&pg=PA29&dq=0.915965594177219015&hl=es&sa=X&ei=uVstU6GGAYLe7AbQ1YGgBg&ved=0CDEQ6AEwAA#v=onepage&q=0.915965594177219015&f=false
|year= 2001
|publisher= Kluwer Academic Publishers
|isbn= 0-7923-7054-6
|page= 30
}}</ref><ref>{{cite book
|author= E. Catalan
|title= Mémoire sur la transformation des séries, et sur quelques intégrales définies, Comptes rendus hebdomadaires des séances de l’Académie des sciences 59
|url= http://books.google.de/books?id=LXZFAAAAcAAJ&pg=PA618
|year= 1864
|publisher= Kluwer Academic éditeurs
|page= 618
}}</ref>
||<br><br><br>
| bgcolor=#e0f0f0 align=center|<math>{C}</math>
|| <math> \int_0^1 \!\! \int_0^1 \!\! \frac{1}{1{+}x^2 y^2}\, dx \,dy
= \! \sum_{n = 0}^\infty \! \frac{(-1)^n}{(2n{+}1)^2} \!
= \! \frac{1}{1^2}{-}\frac{1}{3^2}{+}{\cdots} </math>
||Sum[n=0 to ∞]<br>{(-1)^n/(2n+1)^2}
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A006752}}
||[0;1,10,1,8,1,88,4,1,1,7,22,1,2,3,26,1,11,...]
||1864
||<small> 0.91596559417721901505460351493238411 </small>
|-

<!-------------------------------------------v------------------------------------------->
|0.78539 81633 97448 30961 <ref group=Mw>{{MathWorld|DirichletBetaFunction|Dirichlet Beta Function}}</ref>
||Beta(1) <ref>{{cite book
|author=  Lennart Råde,Bertil 
|title= Mathematics Handbook for Science and Engineering
|page= 423
|year= 2000
|editor= Springer-Verlag
|isbn= 3-540-21141-1
|url= http://books.google.com/books?id=zHEjWAgv7joC&lpg=PA423&dq=0.785398163&hl=es&pg=PA423#v=onepage&q=0.785398163&f=false
}}</ref>
||[[Image:Loglogisticcdf.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\beta}(1)</math>
||<math>\frac{\pi}{4} = \sum_{n = 0}^\infty \frac{(-1)^n}{2n+1} = \frac{1}{1} - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} - \cdots</math>
||Sum[n=0 to ∞]<br>{(-1)^n/(2n+1)}
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A003881}}
||[0; 1,3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,1,1,10,...]
||1805 <br> to <br> 1859
||<small> 0.78539816339744830961566084581987572 </small> 
|-

<!-------------------------------------------v----------------------------------------->
|0.00131 76411 54853 17810 <ref group=Mw>{{MathWorld|Heath-Brown-MorozConstant|Heath-Brown-Moroz Constant}}</ref>
||[[Heath-Brown–Moroz constant]]<ref>{{cite book 
|author= J. B. Friedlander, A. Perelli, C. Viola, D.R. Heath-Brown, H.Iwaniec, J. Kaczorowski
|title= Analytic Number Theory
|url= http://books.google.com/books?id=NuDimaRIVVsC&lpg=PA29&dq=%22Heath-Brown%20and%20Moroz%22&hl=es&pg=PA29#v=onepage&q=%22Heath-Brown%20and%20Moroz%22&f=false
|year= 2002
|editor= Springer
|isbn= 978-3-540-36363-7 
|page= 29
}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{C_{_{HBM}}}</math>
||<math>\underset{p_n: \, {prime}}{\prod_{n = 1}^\infty \left(1-\frac{1}{p_n}\right)^7\left(1+\frac{7p_n+1}{p_n^2}\right)} </math>
||N[prod[n=1 to ∞] <br> {((1-1/prime(n))^7) <br> *(1+(7*prime(n)+1) <br> /(prime(n)^2))}]
|style="text-align:center;"|'''''[[Transcendental number|T]]''''' ?
||{{OEIS2C|A118228}}
||[0,0,1,3,1,7,6,4,1,1,5,4,8,5,3,1,7,8,1,0,9,8,1,...]
||
||<small> 0.00131764115485317810981735232251358 </small>
|-

<!-------------------------------------------v------------------------------------------->
|0.56755 51633 06957 82538
||Module of <br> Infinite <br> [[Tetration]] of ''i''
||
| bgcolor=#e0f0f0 align=center|<math>|{}^\infty {i} | </math>
||<math> \lim_{n \to \infty} \left | {}^n i \right |  =\left | \lim_{n \to \infty}  \underbrace{i^{i^{\cdot^{\cdot^{i}}}}}_n  \right |</math>
||Mod(i^i^i^...)
||
||{{OEIS2C|A212479}}
||[0;1,1,3,4,1,58,12,1,51,1,4,12,1,1,2,2,3,...]
||
||<small> 0.56755516330695782538461314419245334 </small>
|-

<!--------------------------------------------v----------------------------------------->
|0.78343 05107 12134 40705 <ref group=Mw>{{MathWorld|SophomoresDream|Sophomore's Dream}}</ref>
||[[Sophomore's dream]] <sub>1</sub> J.[[Johann Bernoulli|Bernoulli]] <ref>{{cite book 
|author= William Dunham
|title= The Calculus Gallery: Masterpieces from Newton to Lebesgue
|url= http://books.google.com/books?id=QnXSqvTiEjYC&pg=PA51&lpg=PA51&dq=0.7834305107&source=bl&ots=9WOKLh10eD&sig=TlJGSUUYXOpHBTx_1Hm1uXiWDY0&hl=es&sa=X&ei=n9ZBU_uINYPt0gWH3YHIDg&redir_esc=y#v=onepage&q=0.7834305107&f=false
|year= 2005 
|editor= Princeton University Press
|isbn= 978-0-691-09565-3
|page= 51
}}</ref>
||[[File:Socd 002.png|100px]]
| bgcolor=#e0f0f0 align=center|<math>{I}_{1}</math>
||<math>\int_0^1 \! x^{x}\,dx = \sum_{n = 1}^\infty \frac{(-1)^{n+1}}{n^n} = \frac{1}{1^1} - \frac{1}{2^2} + \frac{1}{3^3} - {\cdots} </math>
||Sum[n=1 to ∞] <br> {-(-1)^n /n^n}
||
||{{OEIS2C|A083648}}
||[0;1,3,1,1,1,1,1,1,2,4,7,2,1,2,1,1,1,2,1,14,...]
||1697
||<small> 0.78343051071213440705926438652697546 </small>
|-

<!-------------------------------------------v------------------------------------------->
|1.29128 59970 62663 54040 <ref group=Mw>{{MathWorld|SophomoresDream|Sophomore's Dream}}</ref>
||[[Sophomore's dream]] <sub>2</sub> J.[[Johann Bernoulli|Bernoulli]] <ref>{{cite book 
|author= Jean Jacquelin
|title= SOPHOMORE'S DREAM FUNCTION
|url= http://math.eretrandre.org/tetrationforum/attachment.php?aid=788
|year= 2010
|editor= 
|isbn= 
|page= 
}}</ref>
||[[File:Socd 001.png|100px]]
| bgcolor=#e0f0f0 align=center|<math>{I}_{2}</math>
||<math> \int_0^1 \! \frac{1}{x^x}\, dx 
= \sum_{n = 1}^\infty \frac{1}{n^n} =  \frac{1}{1^1} + \frac{1}{2^2} + \frac{1}{3^3}  + \frac{1}{4^4}+ \cdots</math>
||Sum[n=1 to ∞] <br> {1/(n^n)}
||
||{{OEIS2C|A073009}}
||[1;3,2,3,4,3,1,2,1,1,6,7,2,5,3,1,2,1,8,1,2,4,...]
||1697
||<small> 1.29128599706266354040728259059560054 </small>
|-

<!-----------------------------------------v------------------------------------------->
|0.70523 01717 91800 96514 <ref group=Mw>{{MathWorld|Primorial|Primorial}}</ref>
||[[:de:Primorial#Eigenschaften|Primorial]] constant <br> <small> Sum of the product of inverse of primes </small><ref>{{cite book 
|author= Simon Plouffe
|title= Sum of the product of inverse of primes
|url= http://www.plouffe.fr/simon/constants/primeprod.txt
}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{P_\#}</math>
||<math> \underset{ p_n: \, {prime}}{\sum_{n = 1}^\infty \frac{1}{p_n\#} =  \frac{1}{2} + \frac{1}{6} + \frac{1}{30} + \frac{1}{210} + ... = \sum_{k = 1}^\infty \prod_{n = 1}^k \frac {1}{p_n}}   </math>
||Sum[k=1 to ∞] <br> (prod[n=1 to k] {1/prime(n)})
||
||{{OEIS2C|A064648}}
||[0;1,2,2,1,1,4,1,2,1,1,6,13,1,4,1,16,6,1,1,4,...]
||
||<small> 0.70523017179180096514743168288824851 </small>
|-

<!-----------------------------------------v------------------------------------------->
|0.14758 36176 50433 27417 <ref group=Mw>{{MathWorld|PlouffesConstants|Plouffe's Constants}}</ref>
||[[Bailey–Borwein–Plouffe formula#The BBP formula for π|Plouffe's gamma constant]] <ref>{{cite book 
|author= Simon Plouffe
|title= The Computation of Certain Numbers Using a Ruler and Compass
|url= https://cs.uwaterloo.ca/journals/JIS/compass.html
|page= Vol. 1 (1998), Article 98.1.3
|year= 1998
|editor= Université du Québec à Montréal
}}</ref>
||[[File:Trigo-arctan-animation.gif|100px]]
| bgcolor=#e0f0f0 align=center|<math>{{C}}</math>
||<math> \frac{1}{\pi} \arctan {\frac{1}{2}} 
= \frac{1}{\pi}\sum_{n=0}^\infty \frac {(-1)^n}{(2^{2n+1})(2n+1)}
</math><br><math>
= \frac{1}{\pi} \left( \frac {1}{2} - \frac {1}{3 \cdot 2^3} +\frac {1}{5 \cdot 2^5} -\frac {1}{7 \cdot 2^7} +\cdots 
\right)</math>
||Arctan(1/2)/pi
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A086203}}
||[0;6,1,3,2,5,1,6,5,3,1,1,2,1,1,2,3,1,2,3,2,2,...]
||
||<small> 0.14758361765043327417540107622474052 </small>
|-

<!------------------------------------------v------------------------------------------>
|0.15915 49430 91895 33576 <ref group=Mw>{{MathWorld|PlouffesConstants|Plouffe's Constants}}</ref>
||Plouffe's A constant <ref>{{cite book 
|author= John Srdjan Petrovic
|title= Advanced Calculus: Theory and Practice
|url= http://books.google.com/books?id=oUfBAQAAQBAJ&lpg=PA65&dq=0.1591549430&hl=es&pg=PA65#v=onepage&q=0.1591549430&f=false 
|page= 65
|editor= CRC Press
|year= 2014
|isbn= 978-1-4665-6563-0
}}</ref>
||<br><br><br>
| bgcolor=#e0f0f0 align=center|<math>{A}</math>
||<math> \frac{1}{2 \pi} </math>
||1/(2 pi)
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A086201}}
||[0;6,3,1,1,7,2,146,3,6,1,1,2,7,5,5,1,4,1,2,42,...]
||
||<small> 0.15915494309189533576888376337251436 </small>
|-

<!-----------------------------------------v------------------------------------------->
|0.29156 09040 30818 78013 <ref group=Mw>{{MathWorld|DominoTiling|Domino Tiling}}</ref>
||Dimer constant 2D, <br> [[Domino tiling]]<ref>{{cite book 
|author= Steven R. Finch
|title= Several Constants Arising in Statistical Mechanics
|url= http://arxiv.org/pdf/math/9810155.pdf
|page= 5
|year= 1999
}}</ref><ref>{{cite book 
|author= Federico Ardila, Richard Stanley
|title= Several Constants Arising in Statistical Mechanics
|url= http://math.sfsu.edu/federico/Articles/teselaciones.pdf
|editor= Department of Mathematics, MIT, Cambridge 
}}</ref>
||[[File:Dominoes tiling 8x8.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\frac{C}{\pi}}</math>
C=[[Catalan's constant|Catalan]]
||<math> \int\limits_{-\pi}^{\pi} \frac{\cosh^{-1}\left(\frac{\sqrt{\cos(t)+3}}{\sqrt2}\right)}{4\pi}\,dt </math>
||N[int[-pi to pi] {arccosh(sqrt(<br>cos(t)+3)/sqrt(2))<br>/(4*Pi)dt}]
||
||{{OEIS2C|A143233}}
||[0;3,2,3,16,8,10,3,1,1,2,1,3,1,2,13,1,1,4,1,5,...]
||
||<small> 0.29156090403081878013838445646839491 </small>
|-

<!--------------------------------------------v----------------------------------------->
|0.49801 56681 18356 04271 <br>
0.15494 98283 01810 68512 i
||[[Factorial]](''i'')<ref>{{cite book 
|author= Andrija S. Radovic
|title= A REPRESENTATION OF FACTORIAL FUNCTION, THE NATURE OF CONSTAT AND A WAY FOR SOLVING OF FUNCTIONAL EQUATION F(x) = x . F(x - 1)
|url= http://www.andrijar.com/gamma/gammae.pdf
}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{i}\,!</math>
||<math> \Gamma (1+i) = i \, \Gamma (i) = \int\limits_0^\infty \frac{t^i}{e^t} \mathrm{d} t</math>
||Integral_0^∞ <br> t^i/e^t dt
|style="text-align:center;"|'''''[[Complex number|C]]'''''
||{{OEIS2C|A212877}} <br> {{OEIS2C|A212878}}
||[0;6,2,4,1,8,1,46,2,2,3,5,1,10,7,5,1,7,2,...] <br> - [0;2,125,2,18,1,2,1,1,19,1,1,1,2,3,34,...] ''i''
||
||<small> 0.49801566811835604271369111746219809 <br> - 0.15494982830181068512495513048388 ''i'' </small>
|-

<!-----------------------------------------v-------------------------------------------->
|2.09455 14815 42326 59148 <ref group=Mw>{{MathWorld|WallissConstant|Wallis's Constant}}</ref>
||[[John Wallis|Wallis]] Constant
||[[File:Wallis's Constant.png|100px]]
| bgcolor=#e0f0f0 align=center|<math> W </math>
||<math> \sqrt[3]{\frac{45-\sqrt{1929}}{18}}+\sqrt[3]{\frac{45+\sqrt{1929}}{18}}</math>
||(((45-sqrt(1929)) <br> /18))^(1/3)+ <br> (((45+sqrt(1929)) <br> /18))^(1/3)
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A007493}}
||[2;10,1,1,2,1,3,1,1,12,3,5,1,1,2,1,6,1,11,4,...]
||1616 <br> to <br> 1703
||<small> 2.09455148154232659148238654057930296 </small>
|-

<!-----------------------------------------v------------------------------------------->
|0.72364 84022 98200 00940 <ref group=Mw>{{MathWorld|SarnaksConstant|Sarnak's Constant}}</ref>
||Sarnak constant
||
| bgcolor=#e0f0f0 align=center|<math>{C_{sa} }</math>
||<math> \prod_{p>2} \Big(1 - \frac{p+2}{p^3}\Big) </math>
||N[prod[k=2 to ∞] <br> {1-(prime(k)+2) <br> /(prime(k)^3)}]
|style="text-align:center;"|'''''[[Transcendental number|T]]''''' ?
||{{OEIS2C|A065476}}
||[0;1,2,1,1,1,1,1,1,1,4,4,1,1,1,1,1,1,1,8,2,1,1,...]
||
||<small> 0.72364840229820000940884914980912759 </small>
|-

<!----------------------------------------v-------------------------------------------->
|0.63212 05588 28557 67840 <ref group=Mw>{{MathWorld|e|e}}</ref>
||[[Time constant]] <ref>{{cite book 
|author= Kunihiko Kaneko,Ichiro Tsuda
|title= Complex Systems: Chaos and Beyond 
|url= http://books.google.com/books?id=7lcINfgupggC&lpg=PA211&dq=0.63212&hl=es&pg=PA208#v=onepage&q=0.63212&f=false
|isbn= 3-540-67202-8
|page= 211
|year= 1997
}}</ref>
||[[File:Seq1.png|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\tau}</math>
||<math>  \lim_{n \to \infty} 1-\frac {!n}{n!}=\lim_{n \to \infty} P(n)= \int_{0}^{1}e^{-x}dx = 1{-}\frac{1}{e} = </math> <br>
<math> \sum \limits_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!} =
\frac{1}{1!}{-}\frac{1}{2!}{+}\frac{1}{3!}{-}\frac{1}{4!}{+}\frac{1}{5!}{-}\frac{1}{6!}{+}\cdots </math>
||lim_(n->∞) (1- !n/n!) <br> !n=subfactorial
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A068996}}
||[0;1,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...] <br> = [0;1,{{overline|1,1,2n}}], n∈ℕ 
||
||<small> 0.63212055882855767840447622983853913 </small>
|-

<!-------------------------------------------v------------------------------------------>
|1.04633 50667 70503 18098
||Minkowski-Siegel mass constant <ref>{{cite book 
|author= Steven Finch
|title= Minkowski-Siegel Mass Constants
|page= 5
|year= 2005
|editor= Harvard University
|url= http://www.people.fas.harvard.edu/~sfinch/csolve/ms.pdf
}}</ref> 
||
| bgcolor=#e0f0f0 align=center|<math> F_1 </math>
||<math> \prod_{n=1}^{\infty} \frac{n!}{\sqrt{2\pi n}\left(\frac{n}{e}\right)^n \sqrt[12]{1+\tfrac1{n}}}</math>
||N[prod[n=1 to ∞] <br> n! /(sqrt(2*Pi*n) <br> *(n/e)^n *(1+1/n) <br> ^(1/12))]
||
||{{OEIS2C|A213080}}
||[1;21,1,1,2,1,1,4,2,1,5,7,2,1,20,1,1,1134,3,..]
||1867 <br> 1885 <br> 1935
||<small> 1.04633506677050318098095065697776037 </small>
|-

<!------------------------------------------v------------------------------------------->
|5.24411 51085 84239 62092 <ref group=Mw>{{MathWorld|LemniscateConstant|Lemniscate Constant}}</ref>
||Lemniscate Constant <ref>{{cite book 
|author= 
|title= Evaluation of the complete elliptic integrals by the agm method 
|url= http://www2.mae.ufl.edu/~uhk/AGM-2012.pdf
|isbn= 
|editor= University of Florida, Department of Mechanical and Aerospace Engineering
|page=
|year=
}}</ref>
||<center>[[File:Lemniscate of Bernoulli.gif|80px]]</center>
| bgcolor=#e0f0f0 align=center|<math>2\varpi</math>
||<math>\frac{[\Gamma(\tfrac14)]^2}{\sqrt{2 \pi}} = 
4\int^1_0 \frac{dx}{\sqrt{(1-x^2)(2-x^2)}} </math>
||Gamma[ 1/4 ]^2 <br> /Sqrt[ 2 Pi ]
||
|{{OEIS2C|A064853}}
||[5;4,10,2,1,2,3,29,4,1,2,1,2,1,2,1,4,9,1,4,1,2,...]
||1718
||<small> 5.24411510858423962092967917978223883 </small>
|-

<!--------------------------------------------v----------------------------------------->
|0.66170 71822 67176 23515 <ref group=Mw>{{MathWorld|RobbinsConstant|Robbins Constant}}</ref>
||[[Robbins constant]] <ref>{{cite book
|author= Steven R. Finch
|title= Mathematical Constants
|page= 479
|year= 2003
|editor= Cambridge University Press
|isbn= 3-540-67695-3
|url= http://books.google.com/books?id=Pl5I2ZSI6uAC&pg=PA556&dq=Goh-Schmutz&hl=es&sa=X&ei=db-kUvPWHrCo0AXA8YHgCQ&ved=0CDgQ6AEwAA#v=onepage&q=Schmutz&f=false
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>\Delta(3)</math>
||<math> \frac{4 \! + \! 17\sqrt2 \! -6 \sqrt3 \! -7\pi}{105} \! + \! \frac{\ln(1 \! + \! \sqrt2)}{5} \! + \! \frac{2\ln(2 \! + \! \sqrt3)}{5} </math>
||(4+17*2^(1/2)-6 <br> *3^(1/2)+21*ln(1+ <br> 2^(1/2))+42*ln(2+ <br> 3^(1/2))-7*Pi)/105
|
||{{OEIS2C|A073012}}
||[0;1,1,1,21,1,2,1,4,10,1,2,2,1,3,11,1,331,1,4,...]
||1978
||<small> 0.66170718226717623515583113324841358 </small>
|-

<!---------------------------------------v---------------------------------------------->
|1.30357 72690 34296 39125 <ref group=Mw>{{MathWorld|ConwaysConstant|Conway's Constant}}</ref>
||[[Conway constant]] <ref>{{cite book 
|author= Facts On File, Incorporated
|title= Mathematics Frontiers
|url= http://books.google.com/books?id=gmCSpNhXMooC&lpg=PA45&dq=Conway%20Constant&hl=es&pg=PA45#v=onepage&q=Conway%20Constant&f=false
|isbn= 978-0-8160-5427-5
|page= 46
|year= 1997
}}</ref>
||[[File:Conway constant.png|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\lambda}</math>
||<math> \begin{smallmatrix}
x^{71}\quad\ -x^{69}-2x^{68}-x^{67}+2x^{66}+2x^{65}+x^{64}-x^{63}-x^{62}-x^{61}-x^{60}\\
-x^{59}+2x^{58}+5x^{57}+3x^{56}-2x^{55}-10x^{54}-3x^{53}-2x^{52}+6x^{51}+6x^{50}\\
+x^{49}+9x^{48}-3x^{47}-7x^{46}-8x^{45}-8x^{44}+10x^{43}+6x^{42}+8x^{41}-5x^{40}\\
-12x^{39}+7x^{38}-7x^{37}+7x^{36}+x^{35}-3x^{34}+10x^{33}+x^{32}-6x^{31}-2x^{30}\\
-10x^{29}-3x^{28}+2x^{27}+9x^{26}-3x^{25}+14x^{24}-8x^{23}\quad\ -7x^{21}+9x^{20}\\
+3x^{19}\!-4x^{18}\!-10x^{17}\!-7x^{16}\!+12x^{15}\!+7x^{14}\!+2x^{13}\!-12x^{12}\!-4x^{11}\!-2x^{10}\\
+5x^{9}+x^{7}\quad\ -7x^{6}+7x^{5}-4x^{4}+12x^{3}-6x^{2}+3x-6\ =\ 0 \quad\quad\quad
\end{smallmatrix}</math>
||
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||{{OEIS2C|A014715}}
||[1;3,3,2,2,54,5,2,1,16,1,30,1,1,1,2,2,1,14,1,...]
||1987
||<small> 1.30357726903429639125709911215255189 </small>
|-

<!-------------------------------------------v------------------------------------------>
|1.18656 91104 15625 45282 <ref group=Mw>{{MathWorld|LevyConstant|Levy Constant}}</ref>
||[[Khinchin–Lévy constant]]<ref>{{cite book 
|author= Aleksandr I͡Akovlevich Khinchin
|title= Continued Fractions
|url= http://books.google.com/books?id=R7Fp8vytgeAC&pg=PA66
|isbn= 978-0-486-69630-0
|editor= Courier Dover Publications 
|page= 66
|year= 1997
}}</ref>
||<br><br><br>
| bgcolor=#e0f0f0 align=center|<math>{\beta}</math>
||<math>\frac {\pi^2}{12\,\ln 2}</math>
||pi^2 /(12 ln 2)
||
||{{OEIS2C|A100199}}
||[1;5,2,1,3,1,1,28,18,16,3,2,6,2,6,1,1,5,5,9,...]
||1935
||<small> 1.18656911041562545282172297594723712 </small>
|-

<!------------------------------------------v------------------------------------------->
|0.83564 88482 64721 05333
||[[:ja:ベイカーの定理|Baker constant]] <ref>{{cite book
|author= Jean-Pierre Serre
|title= Travaux de Baker
|page= 74
|year= 1969–1970
|publisher= NUMDAM, Séminaire N. Bourbaki.
|url= http://archive.numdam.org/ARCHIVE/SB/SB_1969-1970__12_/SB_1969-1970__12__73_0/SB_1969-1970__12__73_0.pdf}}</ref>
||[[File:Baker constant.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>\beta_3</math>
||<math>\int^1_0 \frac{{\mathrm{d} t}}{1 + t^3}=\sum_{n = 0}^\infty \frac{(-1)^n}{3n+1}= \frac{1}{3}\left(\ln 2+\frac{\pi}{\sqrt{3}}\right)</math>
||Sum[n=0 to ∞] <br> {((-1)^(n))/(3n+1)}
||
||{{OEIS2C|A113476}}
||[0;1,5,11,1,4,1,6,1,4,1,1,1,2,1,3,2,2,2,2,1,3,...]
||
||<small> 0.83564884826472105333710345970011076 </small>
|-

<!------------------------------------------v------------------------------------------->
|23.10344 79094 20541 6160 <ref group=Mw>{{MathWorld|KempnerSeries|Kempner Series}}</ref>
||[[:de:Kempner-Reihe|Kempner Serie]](0) <ref>{{cite book
|author= Julian Havil
|title= Gamma: Exploring Euler's Constant
|url=http://books.google.com/books?id=7-sDtIy8MNIC&lpg=PA31&dq=Gamma%3A%20Exploring%20Euler's%20Constant%2C%20Julian%20Havil%2C%20Kempner&hl=es&pg=PA31#v=onepage&q=Gamma:%20Exploring%20Euler's%20Constant,%20Julian%20Havil,%20Kempner&f=false
|year= 2003 
|publisher= Princeton University Press
|isbn= 9780691141336 
|page= 31
}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{K_0}</math>
||<math>1{+}\frac12{+}\frac13{+}\cdots{+}\frac19{+}\frac1{11}{+}\cdots{+}\frac1{19}{+}\frac1{21}{+}\cdots{+}\,\text{etc.}</math>
<math>{+}\frac1{99}{+}\frac1{111}{+}\cdots{+}\frac1{119}{+}\frac1{121}{+}\cdots\;\;
\overset {Excluding \; all}{ \underset{ containing \; 0.}{\scriptstyle denominators} }
</math>
||1+1/2+1/3+1/4+1/5<br>+1/6+1/7+1/8+1/9<br>+1/11+1/12+1/13<br>+1/14+1/15+...
||
||{{OEIS2C|A082839}}
||[23;9,1,2,3244,1,1,5,1,2,2,8,3,1,1,6,1,84,1,...]
||
||<small> 23.1034479094205416160340540433255981 </small>
|-

<!----------------------------------------------v--------------------------------------->
|0.98943 12738 31146 95174 <ref group=Mw>{{MathWorld|LebesgueConstants|Lebesgue Constants}}</ref>
||[[Lebesgue constant (interpolation)|Lebesgue constant]] <ref>{{cite book 
|author= Horst Alzer
|title= Journal of Computational and Applied Mathematics, Volume 139, Issue 2
|url= http://ac.els-cdn.com/S0377042701004265/1-s2.0-S0377042701004265-main.pdf?_tid=c20cf466-f4bf-11e3-bd9c-00000aacb362&acdnat=1402859198_57de7868bcc50086f092c66898ec6a33
|year= 2002
|publisher= Elsevier
|isbn= 
|pages= 215–230 
}}</ref> 
||[[File:Fourier synthesis.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math>{C_1}</math>
||<math>\lim_{n\to\infty}\!\! \left(\!{L_n{-}\frac{4}{\pi^2}\ln(2n{+}1)}\!\!\right)\!{=}
\frac{4}{\pi^2}\!\left({\sum_{k=1}^\infty \!\frac{2\ln k}{4k^2{-}1}}
{-}\frac{\Gamma'(\tfrac12)}{\Gamma(\tfrac12)}\!\!\right)</math>
||4/pi^2*[(2 <br> Sum[k=1 to ∞] <br> {ln(k)/(4*k^2-1)}) <br> -poligamma(1/2)]
||
||{{OEIS2C|A243277}}
||[0;1,93,1,1,1,1,1,1,1,7,1,12,2,15,1,2,7,2,1,5,...]
||?
||<small> 0.98943127383114695174164880901886671 </small>
|-

<!------------------------------------------v------------------------------------------->
|0.19452 80494 65325 11361 <ref group=Mw>{{MathWorld|DuBoisReymondConstants|Du Bois Reymond Constants}}</ref>
||[[:es:Constante Du Bois Reymond|2nd du Bois-Reymond constant]] <ref>{{cite book 
|author= Steven R. Finch 
|title= Mathematical Constants
|url=
|year= 2003 
|publisher= Cambridge University Press
|isbn= 3-540-67695-3
|page= 238
}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{C_2}</math>
||<math>\frac{e^2-7}{2} = \int_0^\infty \left|{\frac{d}{dt}\left(\frac{\sin t}{t}\right)^n}\right|\,dt-1 </math>
||(e^2-7)/2 
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A062546}}
||[0;5,7,9,11,13,15,17,19,21,23,25,27,29,31,...]<br> = [0;{{overline|2p+3}}], p∈ℕ
||
||<small> 0.19452804946532511361521373028750390 </small>
|-

<!--------------------------------------------v----------------------------------------->
|0.78853 05659 11508 96106 <ref group=Mw>{{MathWorld|LuerothsConstant|Lüroth's Constant}}</ref>
||Lüroth constant<ref>{{cite book 
|author= Steven Finch
|title= Continued Fraction Transformation III
|url= http://www.people.fas.harvard.edu/~sfinch/csolve/kz3.pdf
|isbn= 
|publisher= Harvard University
|page= 5
|year= 2007
}}</ref>
||<center>[[File:Constante de Lüroth.svg|35px]]</center>
| bgcolor=#e0f0f0 align=center|<math>C_L</math>
||<math>\sum_{n = 2}^\infty \frac{\ln\left(\frac{n}{n-1}\right)}{n}</math>
||Sum[n=2 to ∞] <br> log(n/(n-1))/n
||
|{{OEIS2C|A085361}}
||[0;1,3,1,2,1,2,4,1,127,1,2,2,1,3,8,1,1,2,1,16,...]
||
||<small> 0.78853056591150896106027632216944432 </small>
|-

<!-------------------------------------------v------------------------------------------>
|1.18745 23511 26501 05459 <ref group=Mw>{{MathWorld|FoiasConstant|Foias Constant}}</ref>
||[[Foias constant]] <sub>α</sub> <ref>{{cite book 
|author= Andrei Vernescu
|title= Gazeta Matematica Seria a revista de cultur Matematica Anul XXV(CIV)Nr. 1, Constante de tip Euler generalizate
|url= http://ssmr.ro/gazeta/gma/2007/gma-1-2007.pdf
|year= 2007
|publisher= 
|isbn= 
|page= 14
}}</ref>
||<br><br><br>
|bgcolor=#e0f0f0 align=center|<math>F_\alpha</math>
||<math> x_{n+1} = \left( 1 + \frac{1}{x_n} \right)^n\text{ for }n=1,2,3,\ldots </math>
Foias constant is the unique real number such that if x1 = α then the sequence diverges to ∞. When ''x''<sub>1</sub>&nbsp;=&nbsp;''&alpha;'', <math>\, \lim_{n\to\infty} x_n \tfrac{\log n}{n} = 1 </math>
||
|
||{{OEIS2C|A085848}}
||[1;5,2,1,81,3,2,2,1,1,1,1,1,6,1,1,3,1,1,4,3,2,...]
||2000
||<small> 1.18745235112650105459548015839651935 </small>
|-

<!------------------------------------------v------------------------------------------->
|2.29316 62874 11861 03150 <ref group=Mw>{{MathWorld|FoiasConstant|Foias Constant}}</ref>
||[[Foias constant]] <sub>β</sub> 
||[[File:Foias constant.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>F_\beta</math>
||<math> x^{x+1} = (x+1)^x</math>
||x^(x+1) <br> = (x+1)^x
|
||{{OEIS2C|A085846}}
||[2;3,2,2,3,4,2,3,2,130,1,1,1,1,1,6,3,2,1,15,1,...]
||2000
||<small> 2.29316628741186103150802829125080586 </small>
|-

<!--------------------------------------------v----------------------------------------->
|0.82246 70334 24113 21823 <ref group=Mw>{{MathWorld|Nielsen-RamanujanConstants|Nielsen-Ramanujan Constants}}</ref>
||Nielsen-[[Ramanujan]] constant <ref>{{cite book 
|author= Mauro Fiorentini
|title= Nielsen – Ramanujan (costanti di)
|url= http://bitman.name/math/article/872 
}}</ref>
||<br><br><br>
| bgcolor=#e0f0f0 align=center|<math>\frac{{\zeta}(2)}{2}</math>
||<math> \frac{\pi^2}{12} = \sum_{n=1}^\infty\frac{(-1)^{n+1}}{n^2} = \frac{1}{1^2} {-} \frac{1}{2^2} {+} \frac{1}{3^2} {-} \frac{1}{4^2} {+} \frac{1}{5^2} {-} \cdots </math>
||Sum[n=1 to ∞]<br>{((-1)^(n+1))/n^2}
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A072691}}
||[0;1,4,1,1,1,2,1,1,1,1,3,2,2,4,1,1,1,1,1,1,4...]
||1909
||<small> 0.82246703342411321823620758332301259 </small>
<!-- 0.90689968211710892529703912882107786<br>sqrt(C) = Pi/(2*sqrt(3)) = {{OEIS2C|A093766}} -->
|-

<!------------------------------------------v------------------------------------------->
|0.69314 71805 59945 30941 <ref group=Mw>{{MathWorld|NaturalLogarithmof2|Natural Logarithm of 2}}</ref>
||[[Natural logarithm of 2]] <ref>{{cite book 
|author= Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
|title= Handbook of Continued Fractions for Special Functions
|url= http://books.google.com/books?id=DQtpJaEs4NIC&lpg=PA182&dq=0.6931471805599&hl=es&pg=PA182#v=onepage&q=0.6931471805599&f=false
|year= 2008
|publisher= Springer
|isbn= 978-1-4020-6948-2
|page= 182
}}</ref>
||[[File:Alternating Harmonic Series.PNG|100px]]
| bgcolor=#e0f0f0 align=center|<math>Ln(2)</math>
||<math> \sum_{n=1}^\infty \frac{1}{n 2^n} = 
\sum_{n=1}^\infty \frac{({-}1)^{n+1}}{n} 
= \frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+{\cdots} </math>
||Sum[n=1 to ∞]<br>{(-1)^(n+1)/n}
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A002162}}
||[0;1,2,3,1,6,3,1,1,2,1,1,1,1,3,10,1,1,1,2,1,1,...]
||1550 <br> to <br> 1617
||<small> 0.69314718055994530941723212145817657 </small>
|-

<!-------------------------------------------v------------------------------------------>
|0.47494 93799 87920 65033 <ref group=Mw>{{MathWorld|WeierstrassConstant|Weierstrass Constant}}</ref>
||[[Weierstrass]] constant <ref>{{cite book 
|author= Eric W. Weisstein
|title= CRC Concise Encyclopedia of Mathematics, Second Edition
|url= http://books.google.com/books?id=aFDWuZZslUUC&pg=PA3184&dq=%22Weierstrass+Constant%22&hl=es&sa=X&ei=lGFMU_eWIKTg7QbX9oGAAg&redir_esc=y#v=onepage&q=%22Weierstrass%20Constant%22&f=false
|year= 2003 
|publisher= CRC Press
|isbn= 1-58488-347-2
|page= 151
}}</ref>
||<br><br><br>
| bgcolor=#e0f0f0 align=center|<math>\sigma(\tfrac12)</math>
||<math> \frac{e^{\frac{\pi}{8}}\sqrt{\pi}}{4*2^{3/4} {(\frac {1}{4}!)^2}}</math>
||(E^(Pi/8) Sqrt[Pi])<br> /(4 2^(3/4) (1/4)!^2)
||
||{{OEIS2C|A094692}}
||[0;2,9,2,11,1,6,1,4,6,3,19,9,217,1,2,4,8,6...]
||1872 ?
||<small> 0.47494937998792065033250463632798297 </small>
|-

<!------------------------------------------v------------------------------------------->
|0.57721 56649 01532 86060 <ref group=Mw>{{MathWorld|Euler-MascheroniConstant|Euler-Mascheroni Constant}}</ref>
||[[Euler-Mascheroni constant]]
||[[File:Euler-Mas.jpg|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\gamma}</math>
||<math> \sum_{n=1}^\infty \sum_{k=0}^\infty \frac{(-1)^k}{2^n+k} 
 = \sum_{n=1}^\infty \left(\frac{1}{n} -\ln \left(1+\frac{1}{n}\right)\right) </math> <br> 
<math>= \int_{0}^{1} -\ln \left(\ln \frac{1}{x}\right)\, dx = -\Gamma'(1) = -\Psi(1)</math>
||sum[n=1 to ∞]<br>|sum[k=0 to ∞]<br>{((-1)^k)/(2^n+k)}
||
||{{OEIS2C|A001620}}
||[0;1,1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,1,11,...]
||1735
||<small> 0.57721566490153286060651209008240243 </small>
<!-- 0.42278433509846713939348790991759757<br> ''1-γ'' = {{OEIS2C|A153810}} -->
|-

<!--------------------------------------------v----------------------------------------->
|1.38135 64445 18497 79337
||Beta, Kneser-Mahler polynomial constant<ref>{{cite book 
|author= P. HABEGGER
|title= MULTIPLICATIVE DEPENDENCE AND ISOLATION I
|page= 2
|year= 2003
|publisher= Institut für Mathematik, Universit¨at Basel, Rheinsprung Basel, Switzerland
|url= http://www.math.uni-frankfurt.de/~habegger/multdep1.pdf}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>\beta</math>
||<math> e^{^{\textstyle{\frac{2}{\pi}} \displaystyle{\int_0^{\frac{\pi}{3}}} \textstyle{t \tan t\ dt}}} = 
         e^{^{\displaystyle{\,\int_{\frac{-1}{3}}^{\frac{1}{3}}} \textstyle{\,\ln \lfloor 1+e^{2 \pi i t}} \rfloor dt}}</math>
||<small> e^((PolyGamma(1,4/3) <br> - PolyGamma(1,2/3) <br> +9)/(4*sqrt(3)*Pi)) </small>
|
||{{OEIS2C|A242710}}
||[1;2,1,1,1,1,1,4,1,139,2,1,3,5,16,2,1,1,7,2,1,...]
||1963
||<small> 1.38135644451849779337146695685062412 </small>
|-

<!--------------------------------------------v----------------------------------------->
|1.35845 62741 82988 43520 <ref group=Mw>{{MathWorld|GoldenSpiral|Golden Spiral}}</ref>
||[[Golden Spiral]] 
||[[File:FakeRealLogSpiral.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math> c </math>
||<math> \varphi ^ \frac{2}{\pi} = \left(\frac{1 + \sqrt{5}}{2}\right)^{\frac{2}{\pi}}</math>
||GoldenRatio^(2/pi)
||
|{{OEIS2C|A212224}}
||[1;2,1,3,1,3,10,8,1,1,8,1,15,6,1,3,1,1,2,3,1,1,...]
||
||<small> 1.35845627418298843520618060050187945 </small>
<!-- 0.30634896253003312211567570119977068<br>''ln''(c) = (2/pi)ln(phi) = {{OEIS2C|A212225}} -->
|-

<!--------------------------------------------v----------------------------------------->
|0.57595 99688 92945 43964 <ref group=Mw>{{MathWorld|StephensConstant|Stephen's Constant}}</ref>
||[[Euler product#Notable constants|Stephens constant]] <ref>{{cite book
|author= Steven Finch
|title= Class Number Theory
|pages= 8
|year= 2005
|publisher= Harvard University
|url= http://www.people.fas.harvard.edu/~sfinch/csolve/clss.pdf
}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math> C_S </math>
||<math> \prod_{n = 1}^\infty \left(1 - \frac{p}{p^3-1}\right) </math>
||Prod[n=1 to ∞] <br> {1-hprime(n) <br> /(hprime(n)^3-1)}
|style="text-align:center;"|'''''[[Transcendental number|T]]''''' ?
|{{OEIS2C|A065478}}
||[0;1,1,2,1,3,1,3,1,2,1,77,2,1,1,10,2,1,1,1,7,...]
||?
||<small> 0.57595996889294543964316337549249669 </small>
|-

<!---------------------------------------------v---------------------------------------->
|0.73908 51332 15160 64165 <ref group=Mw>{{MathWorld|DottieNumber|Dottie Number}}</ref>
||[[Fixed point (mathematics)|Dottie number]] <ref>{{cite book 
|author= James Stewart
|title= Single Variable Calculus: Concepts and Contexts
|url= http://books.google.com/books?id=eztUxtCfNXoC&lpg=PP1&dq=Single%20Variable%20Calculus%3A%20Concepts%20and%20Contexts%20%20Escrito%20por%20James%20Stewart&hl=es&pg=PA314#v=onepage&q=Single%20Variable%20Calculus:%20Concepts%20and%20Contexts%20%20Escrito%20por%20James%20Stewart&f=false
|isbn= 978-0-495-55972-6
|publisher= Brooks/Cole
|page= 314
|year= 2010
}}</ref>
||[[File:Dottie number.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>d</math>
||<math> \lim_{x\to \infty} \cos^x(c) = \lim_{x\to \infty} \underbrace{\cos(\cos(\cos(\cdots(\cos(c)))))}_x</math>
||cos(c)=c
||
|{{OEIS2C|A003957}}
||[0;1,2,1,4,1,40,1,9,4,2,1,15,2,12,1,21,1,17,...]
||?
||<small> 0.73908513321516064165531208767387340 </small>
|-

<!-----------------------------------------v-------------------------------------------->
|0.67823 44919 17391 97803 <ref group=Mw>{{MathWorld|EulerProduct|Euler Product}}</ref>
||[[Euler product#Notable constants|Taniguchi constant]] <ref>{{cite book
|author= Steven Finch
|title= Class Number Theory
|page= 8
|year= 2005
|publisher= Harvard University
|url= http://www.people.fas.harvard.edu/~sfinch/csolve/clss.pdf
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math> C_T </math>
||<math> \prod_{n = 1}^\infty \left(1 - \frac{3}{{p_n}^3}+\frac{2}{{p_n}^4}+\frac{1}{{p_n}^5}-\frac{1}{{p_n}^6}\right) </math>
<center><math>\scriptstyle p_{n}= \, \text{prime} </math></center>
||Prod[n=1 to ∞] {1 <br/> -3/ithprime(n)^3 <br/> +2/ithprime(n)^4 <br/> +1/ithprime(n)^5 <br/> -1/ithprime(n)^6}
|style="text-align:center;"|'''''[[Transcendental number|T]]''''' ?
|{{OEIS2C|A175639}}
||[0;1,2,9,3,1,2,9,11,1,13,2,15,1,1,1,2,4,1,1,1,...]
||?
||<small> 0.67823449191739197803553827948289481 </small>
|-

<!------------------------------------------v------------------------------------------->
|1.85407 46773 01371 91843 <ref group=Mw>{{MathWorld|LemniscateCase|Lemniscate Case}}</ref>
||Gauss' Lemniscate constant<ref>{{cite book 
|author= Steven R. Finch 
|title= Mathematical Constants
|url=http://books.google.com/books?id=Pl5I2ZSI6uAC&pg=PA421&lpg=PA421&dq=Gauss%27+lemniscate+constant&source=bl&ots=K0qH3-ky5d&sig=asQRT-YqtApD-8HamOcLokgy9Hs&hl=es&sa=X&ei=I0wmU9f9EoOH0AXty4CwBw&redir_esc=y#v=onepage&q=Gauss%27%20lemniscate%20constant&f=false
|year= 2003 
|publisher= Cambridge University Press
|isbn= 3-540-67695-3
|page= 421
}}</ref>
||[[File:Lemniscate Building.gif|100px]]
|bgcolor=#e0f0f0 align=center|<math> L \text{/}\sqrt{2}</math>
||<math>\int\limits_0^\infty \frac{{\mathrm{d} x}}{\sqrt{1 + x^4}}
 = \frac {1}{4\sqrt{\pi}} \,\Gamma \left(\frac {1}{4}\right)^2
 = \frac{4 \left(\frac {1}{4}!\right)^2} {\sqrt{\pi}}</math>
<center><math>\scriptstyle \Gamma() \text{= Gamma function} </math></center>
||pi^(3/2)/(2 Gamma(3/4)^2)
||
|{{OEIS2C|A093341}}
||[1;1,5,1,5,1,3,1,6,2,1,4,16,3,112,2,1,1,18,1,...]
||
||<small> 1.85407467730137191843385034719526005 </small>
|-

<!------------------------------------------v------------------------------------------->
|1.75874 36279 51184 82469
||Infinite product constant, with Alladi-Grinstead  <ref>{{cite book 
|author= Steven R. Finch 
|title= Mathematical Constants
|url= http://my.safaribooksonline.com/book/math/9781107266582/2-constants-associated-with-number-theory/210_sierpinskis_constant
|year= 2003 
|publisher= Cambridge University Press
|isbn= 3-540-67695-3
|page= 122
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math> Pr_1</math>
||<math> \prod_{n = 2}^\infty \Big(1 + \frac{1}{n}\Big)^\frac{1}{n}</math>
||Prod[n=2 to inf] {(1+1/n)^(1/n)}
||
||{{OEIS2C|A242623}}
||[1;1,3,6,1,8,1,4,3,1,4,1,1,1,6,5,2,40,1,387,2,...]
||1977
||<small> 1.75874362795118482469989684865589317 </small> 
|-

<!--------------------------------------------v----------------------------------------->
|1.86002 50792 21190 30718
||[[Spiral of Theodorus]] <ref>{{cite book
|author= Jorg Waldvogel
|title= Analytic Continuation of the Theodorus Spiral
|pages= 16
|year= 2008
|url= http://www.sam.math.ethz.ch/~joergw/Papers/theopaper.pdf
}}</ref> 
||[[File:Spiral of Theodorus.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math> \partial </math>
||<math> \sum_{n=1}^{\infty} \frac{1}{\sqrt{n^3} + \sqrt{n}} =
\sum_{n=1}^{\infty} \frac{1}{\sqrt{n} (n+1)}</math>
||Sum[n=1 to ∞] <br/> {1/(n^(3/2) <br/> +n^(1/2))}
||
||{{OEIS2C|A226317}}
||[1;1,6,6,1,15,11,5,1,1,1,1,5,3,3,3,2,1,1,2,19,...]
||-460 <br> to <br> -399
||<small> 1.86002507922119030718069591571714332 </small>
|-

<!-------------------------------------------v------------------------------------------>
|2.79128 78474 77920 00329
||[[Nested radical]] S<sub>5</sub> 
||
|bgcolor=#e0f0f0 align=center|<math> S_{5} </math>
||<math>\displaystyle \frac{\sqrt{21}+1}{2} =  
\scriptstyle  \, \sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5+\cdots}}}}}\; </math>
<math> = 1+ \, \scriptstyle \sqrt{5-\sqrt{5-\sqrt{5-\sqrt{5-\sqrt{5-\cdots}}}}}\; </math>
||(sqrt(21)+1)/2
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||[http://oeis.org/A222134 A222134]
||[2;1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,...]<br>[2;{{overline|1,3}}]
||?
||<small> 2.79128784747792000329402359686400424 </small>
|-

<!-------------------------------------------v------------------------------------------>
|0.70710 67811 86547 52440 <br> +0.70710 67811 86547 524 i <ref group=Mw>{{MathWorld|i|i}}</ref>
||[[Square root]] of ''i'' <ref>{{cite book
|author= Robert Kaplan,Ellen Kaplan
|title= The Art of the Infinite: The Pleasures of Mathematics
|year= 2014
|page= 238
|editor= Oxford University Press, Bloomsburv Press
|isbn= 978-1-60819-869-6
|url= http://books.google.com/books?id=KXdvAAAAQBAJ&lpg=PA238&dq=0.707106781&hl=es&pg=PA238#v=onepage&q=0.707106781&f=false
}}</ref> 
||[[File:Imaginary2Root.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math> \sqrt{i} </math>
||<math> \sqrt[4]{-1} = \frac{1+i}{\sqrt{2}} = e^ \frac{i\pi}{4} =
 \cos\left (\frac{\pi}{4} \right ) + i\sin\left ( \frac{\pi}{4} \right ) </math>
||(1+i)/(sqrt 2)
|style="text-align:center;"|'''''[[Complex number|C]] [[Algebraic number|A]]'''''
||{{OEIS2C|A010503}}
||[0;1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,..] <br>= [0;1,{{overline|2}},...] <br>  [0;1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,..] ''i'' <br>= [0;1,{{overline|2}},...] ''i''
||?
||<small> 0.70710678118654752440084436210484903 </small> <br/> <small> + 0.70710678118654752440084436210484 ''i'' </small>
|-

<!----------------------------------------------v--------------------------------------->
|0.80939 40205 40639 13071 <ref group=Mw>{{MathWorld|Alladi-GrinsteadConstant|Alladi-Grinstead Constants}}</ref>
||Alladi–Grinstead constant <ref>{{cite book 
|author= Steven R. Finch 
|title= Mathematical Constants
|url= http://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA121&lpg=PA121&dq=0.8093940205#v=onepage&q=0.8093940205&f=false 
|year= 2003 
|publisher= Cambridge University Press
|isbn= 3-540-67695-3
|page= 121
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{\mathcal{A}_{AG}}</math>
||<math> e^{-1+\sum \limits_{k=2}^\infty \sum \limits_{n=1}^\infty \frac{1}{n k^{n+1}}} = e^{-1-\sum \limits_{k=2}^\infty \frac{1}{k} \ln \left( 1-\frac{1}{k}\right)} </math>
||<small> e^{(sum[k=2 to ∞] <br/> |sum[n=1 to ∞] <br/> {1/(n k^(n+1))})-1} </small>
||
||{{OEIS2C|A085291}}
||[0;1,4,4,17,4,3,2,5,3,1,1,1,1,6,1,1,2,1,22,...] 
||1977
||<small> 0.80939402054063913071793188059409131 </small> 
|-

<!----------------------------------------------v--------------------------------------->
|2.58498 17595 79253 21706 <ref group=Mw>{{MathWorld|SierpinskiConstant|Sierpinski Constant}}</ref>
||[[Sierpiński's constant]] <ref>{{cite book
|author= Eric W. Weisstein 
|title= CRC Concise Encyclopedia of Mathematics, Second Edition
|pages= 1356
|year= 2002
|publisher= CRC Press
|url= http://books.google.com/books?id=aFDWuZZslUUC&pg=PA2685&dq=1.584962500&hl=es&sa=X&ei=Db6rUaP9Aq-M7Ab9sYHADA&redir_esc=y#v=onepage&q=1.584962500&f=false
}}</ref> 
||[[File:Random Sierpinski Triangle animation.gif|100px]]
|bgcolor=#e0f0f0 align=center|<math> {K} </math>
||<math>\pi\left(2\gamma+\ln\frac{4\pi^3}{\Gamma(\tfrac{1}{4})^4}\right) =
  \pi (2 \gamma + 4 \ln\Gamma(\tfrac{3}{4}) - \ln\pi) </math>
<math> = \pi \left(2 \ln 2+3 \ln \pi + 2 \gamma - 4 \ln \Gamma (\tfrac{1}{4})\right)</math>
||-Pi Log[Pi]+2 Pi <br/>  EulerGamma<br/>+4 Pi Log<br/>[Gamma[3/4]]
||
||{{OEIS2C|A062089}}
||[2;1,1,2,2,3,1,3,1,9,2,8,4,1,13,3,1,15,18,1,...]
||1907
||<small> 2.58498175957925321706589358738317116 </small>
|-

<!------------------------------------------v------------------------------------------->
|1.73245 47146 00633 47358 <ref group=Ow>[http://oeis.org/wiki/Euler%E2%80%93Mascheroni_constant Reciprocal of the Euler–Mascheroni constant]</ref>
||Reciprocal of the Euler–Mascheroni constant
||
|bgcolor=#e0f0f0 align=center|<math>\frac {1}{\gamma}</math>
||<math> \left(\int_{0}^{1} -\log \left(\log \frac{1}{x}\right)\, dx\right)^{-1} = \sum_{n=1}^\infty (-1)^n (-1+\gamma)^n </math>
||1/Integrate_ <br/> {x=0 to 1} <br/> -log(log(1/x))
||
||{{OEIS2C|A098907}}
||[1;1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,1,11,...]
||
||<small> 1.73245471460063347358302531586082968 </small> 
|-

<!--------------------------------------------v----------------------------------------->
|1.43599 11241 76917 43235 <ref group=Mw>{{MathWorld|LebesgueConstants|Lebesgue Constants}}</ref>
||[[Lebesgue constant (interpolation)]] <ref>{{cite book 
|author= Chebfun Team
|title= Lebesgue functions and Lebesgue constants
|url= http://www.mathworks.com/matlabcentral/fileexchange/23972-chebfun/content/chebfun/examples/approx/html/LebesgueConst.html
|year= 2010
|publisher= MATLAB Central
|isbn= 
|page= 
}}</ref><ref>{{cite book
|author= Simon J. Smith
|title= Lebesgue constants in polynomial interpolation
|url= http://www.emis.de/journals/AMI/2006/smith
|year= 2005
|publisher= La Trobe University, Bendigo, Australia
|isbn=
|page=
}}</ref>
||[[File:Fourier series integral identities.gif|100px]]
|bgcolor=#e0f0f0 align=center|<math>{L_1}</math>
||<math> \prod_{\begin{smallmatrix}i=0\\ j\neq i\end{smallmatrix}}^{n} \frac{x-x_i}{x_j-x_i} 
= \frac {1}{\pi} \int_0^{\pi} \frac {\lfloor \sin{\frac{3 t}{2}}\rfloor}{\sin{\frac{t}{2}}}\, dt = \frac {1}{3} + \frac {2 \sqrt{3}}{\pi} </math>
||1/3 + 2*sqrt(3)/pi
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A226654}}
||[1;2,3,2,2,6,1,1,1,1,4,1,7,1,1,1,2,1,3,1,2,1,1,...]
||1902 ~
||<small> 1.43599112417691743235598632995927221 </small>
|-

<!----------------------------------------------v--------------------------------------->
|3.24697 96037 17467 06105 <ref group=Mw>{{MathWorld|SilverConstant|Silver Constant}}</ref>
||Silver root <br/> Tutte–Beraha constant <ref>{{cite book 
|author= D. R. Woodall
|title= CHROMATIC POLYNOMIALS OF PLANE TRIANGULATIONS
|page= 5
|year= 2005
|editor= University of Nottingham
|url= https://www.maths.nottingham.ac.uk/personal/drw/PG/cp.hndt.pdf
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math> \varsigma </math>
||<math> 2+2 \cos  \frac {2\pi} 7 = \textstyle 2+\frac{2+\sqrt[3]{7 + 7 \sqrt[3]{7 + 7 \sqrt[3]{\, 7 + \cdots}}}}{1+\sqrt[3]{7 + 7 \sqrt[3]{7 + 7 \sqrt[3]{\, 7 + \cdots}}}}</math>
||2+2 cos(2Pi/7)
<!---2+(2+(7+7(7+7(7+7(7+7(7)^1/3)^1/3)^1/3)^1/3)^1/3)/(1+(7+7(7+7(7+7(7+7(7)^1/3)^1/3)^1/3)^1/3)^1/3)--->
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||{{OEIS2C|A116425}}
||[3;4,20,2,3,1,6,10,5,2,2,1,2,2,1,18,1,1,3,2,...]
||
||<small> 3.24697960371746706105000976800847962 </small>
|-

<!--------------------------------------------v----------------------------------------->
|1.94359 64368 20759 20505 <ref group=Mw>{{MathWorld|TotientSummatoryFunction|Totient Summatory Function}}</ref>
||[[Euler's totient function|Euler Totient <br/> constant]] <ref>{{cite book 
|author= Benjamin Klopsch
|title= NOTE DI MATEMATICA: Representation growth and representation zeta functions of groups
|url= http://poincare.unile.it/adv2013/NOTE_VOL_33.pdf
|year= 2013
|publisher= Universita del Salento
|ISSN= 1590–0932 
|page= 114
}}</ref><ref>{{cite book 
|author= Nikos Bagis
|title= Some New Results on Prime Sums (3 The Euler Totient constant)
|url= http://carma.newcastle.edu.au/jon/Preprints/Papers/Submitted%20Papers/Elliptic%20moments/Papers/bagis.pdf
|year=  
|publisher= Aristotle University of Thessaloniki
|isbn= 
|page= 8
}}</ref>
||[[File:EulerPhi100.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>ET </math>
||<math>  \underset {p \text{= primes}}
{\prod_{p} \Big(1 + \frac{1}{p(p-1)}\Big)} = \frac {\zeta(2)\zeta(3)}{\zeta(6)}=\frac {315 \zeta(3)}{2\pi^4} </math>
||zeta(2)*zeta(3)<br/>/zeta(6)
||
||{{OEIS2C|A082695}}
||[1;1,16,1,2,1,2,3,1,1,3,2,1,8,1,1,1,1,1,1,1,32,...]
||1750
||<small> 1.94359643682075920505707036257476343 </small>
|-

<!--------------------------------------------v----------------------------------------->
|1.49534 87812 21220 54191
||Fourth root of five <ref>{{cite book 
|author= Robinson, H.P.
|title= MATHEMATICAL CONSTANTS.
|url= http://www.escholarship.org/uc/item/2t95c0bp
|year= 1971–2011
|publisher= Lawrence Berkeley National Laboratory
|isbn= 
|page= 40
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>\sqrt[4]{5} </math>
||<math> \sqrt[5]{5 \,\sqrt[5]{5 \, \sqrt[5]{5 \,\sqrt[5]{5 \,\sqrt[5]{5  \,\cdots}}}}} </math>
||(5(5(5(5(5(5(5) <br/> ^1/5)^1/5)^1/5) <br/> ^1/5)^1/5)^1/5) <br/> ^1/5 ...
|style="text-align:center;"|'''''[[Irrational number|I]]'''''
||{{OEIS2C|A011003}}
||[1;2,53,4,96,2,1,6,2,2,2,6,1,4,1,49,17,2,3,2,...]
||
||<small> 1.49534878122122054191189899414091339 </small>
|-

<!------------------------------------------v------------------------------------------->
|0.87228 40410 65627 97617 <ref group=Mw>{{MathWorld|FordCircle|Ford Circle}}</ref>
||Area of [[Ford circle]] <ref>{{cite book
|author= Annmarie McGonagle
|title= A New Parameterization for Ford Circles
|pages= 
|year= 2011
|publisher= Plattsburgh State University of New York
|url= http://www.plattsburgh.edu/files/686/files/Mcgonaglevol%205p34-44.pdf
}}</ref> 
||[[File:Circumferències de Ford.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math> A_{CF} </math>
||<math> 
\sum_{q\ge 1} \sum_{ (p, q)=1 \atop 1 \le p < q }\pi \left( \frac{1}{2 q^2} \right)^2 
\underset {\zeta() \text{= Riemann Zeta Function}}
{= \frac{\pi}{4} \frac{\zeta(3)}{\zeta(4)}
= \frac{45}{2} \frac{\zeta(3)}{\pi^3}}
</math>
||pi Zeta(3) /(4 Zeta(4))
||
||
||[0;1,6,1,4,1,7,5,36,3,29,1,1,10,3,2,8,1,1,1,3,...]
||
||<small> 0.87228404106562797617519753217122587 </small>
|-

<!---------------------------------------------v---------------------------------------->
|1.08232 32337 11138 19151 <ref group=Mw>{{MathWorld|RiemannZetaFunction|Riemann Zeta Function}}</ref>
||Zeta(4) <ref>{{cite book 
|author= V. S. Varadarajan
|title= Euler Through Time: A New Look at Old Themes
|url= http://books.google.com/books?id=CYyKTREGYd0C&pg=PA60&dq=1.08232323371113819&hl=es&sa=X&ei=PP__UrTNH6vA7AaTroHoDw&redir_esc=y#v=onepage&q=1.08232323371113819&f=false
|year= 2000 
|publisher= AMS
|isbn= 0-8218-3580-7
|page= 
}}</ref>
||<br><br><br>
|bgcolor=#e0f0f0 align=center|<math>\zeta(4)</math>
||<math> \frac{\pi^4}{90} = \sum_{n=1}^\infty\frac{{1}}{n^4} = \frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \frac{1}{4^4} + \frac{1}{5^4} + ... </math>
||Sum[n=1 to ∞]<br/>{1/n^4}
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A013662}}
||[1;12,6,1,3,1,4,183,1,1,2,1,3,1,1,5,4,2,7,23,...]
||?
||<small> 1.08232323371113819151600369654116790 </small>
|-

<!---------------------------------------------v---------------------------------------->
|1.56155 28128 08830 27491  
<!--- The [[Triangular number#Triangular roots and tests for triangular numbers|Triangular root]] of 2--->
||[[Square triangular number|Triangular root]] of 2.<ref>{{cite book 
|author= Leonhard Euler, Joseph Louis Lagrange
|title= Elements of Algebra, Volumen 1
|url= http://books.google.com/books?id=hqI-AAAAYAAJ&pg=PA334&dq=%22triangular+root%22&hl=es&sa=X&ei=8tf3UtSGM8zT7Aag2YGgDw&redir_esc=y#v=onepage&q=%22triangular%20root%22&f=false
|year= 1810
|publisher= J. Johnson and Company
|isbn= 
|page= 333
}}</ref> 
||[[File:Números triangulares.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>{R_2}</math>
||<math>\frac{\sqrt{17}-1}{2} = \,\scriptstyle \sqrt{4+\sqrt{4+\sqrt{4+\sqrt{4+\sqrt{4+\sqrt{4+\cdots}}}}}} \,\, -1 </math>
<math> = \,\scriptstyle \sqrt{4-\sqrt{4-\sqrt{4-\sqrt{4-\sqrt{4-\sqrt{4-\cdots}}}}}} \textstyle </math>
||(sqrt(17)-1)/2
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||{{OEIS2C|A222133}}
||[1;1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,...] <br> [1;{{overline|1,1,3}}]
||
||<small> 1.56155281280883027491070492798703851 </small>
|-

<!-------------------------------------------v------------------------------------------>
|9.86960 44010 89358 61883
||Pi Squared
||<br><br><br>
|bgcolor=#e0f0f0 align=center|<math>{\pi} ^2</math>
||<math>6\, \zeta(2) = 6 \sum_{n=1}^\infty \frac{1}{n^2} = \frac{6}{1^2} + \frac{6}{2^2} + \frac{6}{3^2} + \frac{6}{4^2}+ \cdots</math>
||6 Sum[n=1 to ∞]<br/>{1/n^2}
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||[http://oeis.org/A002388 A002388]
||[9;1,6,1,2,47,1,8,1,1,2,2,1,1,8,3,1,10,5,1,3,...]
||
||<small> 9.86960440108935861883449099987615114 </small>
|-

<!---------------------------------------------v---------------------------------------->
|1.32471 79572 44746 02596 <ref group=Mw>{{MathWorld|PlasticConstant|Plastic Constant}}</ref>
||[[Plastic number]] <ref>{{cite book 
|author= Ian Stewart
|title= Professor Stewart's Cabinet of Mathematical Curiosities
|url= http://books.google.com/books?id=oW6Xeo8EmDgC&pg=PT120&dq=%22Plastic+number%22&hl=es&sa=X&ei=FereUv76CoS74AS4tYDoAQ&ved=0CEIQ6AEwAg#v=onepage&q=%22Plastic%20number%22&f=false
|year= 1996
|publisher= Birkhäuser Verlag
|isbn= 978-1-84765-128-0
|page= 
}}</ref>
||[[File:Nombre plastique.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{\rho}</math>
||<math>\sqrt[3]{1 + \! \sqrt[3]{1 + \! \sqrt[3]{1 + \cdots}}} = \textstyle \sqrt[3]{\frac{1}{2}+ \! \sqrt{\frac{23}{108}}}+ \! \sqrt[3]{\frac{1}{2}- \! \sqrt{\frac{23}{108}}}</math>
||<small>(1+(1+(1+(1+(1+(1 <br/> )^(1/3))^(1/3))^(1/3))<br/>^(1/3))^(1/3))^(1/3) </small>
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||{{OEIS2C|A060006}}
||[1;3,12,1,1,3,2,3,2,4,2,141,80,2,5,1,2,8,2,...]
||1929
||<small> 1.32471795724474602596090885447809734 </small>
|-

<!------------------------------------------v------------------------------------------->
|2.37313 82208 31250 90564
||Lévy <sub>2</sub> constant <ref>{{cite book 
|author= H.M. Antia
|title= Numerical Methods for Scientists and Engineers
|url= http://books.google.com/books?id=YzXsZgjyFA4C&pg=PA220&dq=1.772453850905516&hl=es&sa=X&ei=MbMnUuOzBcvT7AbdyoHoBA&ved=0CDIQ6AEwAA#v=onepage&q=1.772453850905516&f=false
|year= 2000
|publisher= Birkhäuser Verlag
|isbn= 3-7643-6715-6
|page= 220
}}</ref>
||<br><br><br>
|bgcolor=#e0f0f0 align=center|<math>2\,ln\,\gamma </math>
||<math>\frac{\pi^2}{6ln(2)} </math>
||Pi^(2)/(6*ln(2))
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A174606}}
||[2;2,1,2,8,57,9,32,1,1,2,1,2,1,2,1,2,1,3,2,...]
||1936
||<small> 2.37313822083125090564344595189447424 </small>
|-

<!------------------------------------------v------------------------------------------->
|0.85073 61882 01867 26036 <ref group=Mw>{{MathWorld|PaperFoldingConstant|Paper Folding Constant}}</ref>
||[[Regular paperfolding sequence]] <ref>{{cite book  
|author= Francisco J. Aragón Artacho, David H. Baileyy, Jonathan M. Borweinz, Peter B. Borwein
|title= Tools for visualizing real numbers.
|url= http://carma.newcastle.edu.au/jon/tools1.pdf
|year= 2012
|publisher= 
|isbn= 
|page= 33
}}</ref><ref>{{cite book
|author= 
|title= Papierfalten
|url= http://www.jgiesen.de/Divers/PapierFalten/PapierFalten.pdf
|year= 1998
|publisher= 
|isbn= 
|page= 
}}</ref>
||[[File:Miura-ori.gif|100px]]
|bgcolor=#e0f0f0 align=center|<math>{P_f}</math>
||<math> \sum_{n=0}^{\infty} \frac {8^{2^n}}{2^{2^{n+2}}-1} = 
\sum_{n=0}^{\infty} \cfrac {\tfrac {1}{2^{2^n}}} {1-\tfrac{1}{2^{2^{n+2}}}} </math>
||<small> N[Sum[n=0 to ∞]</small> <br/> {8^2^n/(2^2^ <br/> (n+2)-1)},37]
||
||{{OEIS2C|A143347}}
||[0;1,5,1,2,3,21,1,4,107,7,5,2,1,2,1,1,2,1,6,...]
||
||<small> 0.85073618820186726036779776053206660 </small>
|-

<!------------------------------------------v------------------------------------------->
|1.15636 26843 32269 71685 <ref group=Mw>{{MathWorld|PaperFoldingConstant|Paper Folding Constant}}</ref>
||Cubic recurrence constant <ref>{{cite journal 
|title= The generalized-Euler-constant function γ(z) and a generalization of Somos's quadratic recurrence constant
|year= 2008 
|first1= Jonathan |last1=Sondow 
|first2= Petros|last2= Hadjicostas 
|doi= 10.1016/j.jmaa.2006.09.081 
|journal= Journal of Mathematical Analysis and Applications 
|volume= 332 
|pages= 292–314
|arxiv=math/0610499
}}</ref><ref>{{cite book
|author= J. Sondow.
|title= Generalization of Somos Quadratic
|url= http://arxiv.org/pdf/math/0610499.pdf
}}</ref>
||<br><br><br>
|bgcolor=#e0f0f0 align=center|<math>{\sigma_3}</math>
||<math>\prod_{n=1}^\infty n^{{3}^{-n}} = \sqrt[3] {1 \sqrt[3] {2 \sqrt[3]{3 \cdots}}} = 1^{1/3} \; 2^{1/9} \; 3^{1/27} \cdots </math>
||prod[n=1 to ∞]<br/>{n ^(1/3)^n}
||
||{{OEIS2C|A123852}}
||[1;6,2,1,1,8,13,1,3,2,2,6,2,1,2,1,1,1,10,33,...]
||
||<small> 1.15636268433226971685337032288736935 </small>
|-

<!-------------------------------------------v------------------------------------------>
|1.26185 95071 42914 87419 <ref group=Mw>{{MathWorld|KochSnowflake|Koch Snowflake}}</ref>
||Fractal dimension of the [[Koch snowflake]] <ref>{{cite book 
|author= Chan Wei Ting ...
|title= Moire patterns + fractals
|pages= 16
|url= http://www.math.nus.edu.sg/aslaksen/gem-projects/maa/0304-2-02-Moire_Patterns_and_Fractals.pdf
}}</ref> 
||[[File:Koch snowflake05.ogv|100px]]
|bgcolor=#e0f0f0 align=center|<math>{C_k}</math>
||<math> \frac{\log 4}{\log 3} </math>
||log(4)/log(3)
|style="text-align:center;"|'''''[[Irrational number|I]]'''''
||[http://oeis.org/A100831 A100831]
||[1;3,1,4,1,1,11,1,46,1,5,112,1,1,1,1,1,3,1,7,...]
||
||<small> 1.26185950714291487419905422868552171 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|6.58088 59910 17920 97085
||Froda constant<ref>{{cite book 
|author= Christoph Zurnieden
|title= Descriptions of the Algorithms
|url= http://pragmath.sourceforge.net/algorithms.pdf
|year= 2008 
|publisher= 
|isbn= 
|page= 
}}</ref>
||<br><br>
|bgcolor=#e0f0f0 align=center|<math>2^{\,e} </math>
||<math>2^e  </math>
||2^e
||
||
||[6;1,1,2,1,1,2,3,1,14,11,4,3,1,1,7,5,5,2,7,...]
||
||<small> 6.58088599101792097085154240388648649 </small>
|-

<!-----------------------------------------v-------------------------------------------->
|0.26149 72128 47642 78375 <ref group=Mw>{{MathWorld|MertensConstant|Mertens Constant}}</ref>
||[[Meissel-Mertens constant]] <ref>{{cite book 
|author= Julian Havil
|title= Gamma: Exploring Euler's Constant
|url=http://books.google.com/?id=7-sDtIy8MNIC&pg=PA161&dq=Khinchin%27s+constant#v=onepage&q=Khinchin%27s%20constant&f=false
|year= 2003 
|publisher= Princeton University Press
|isbn= 9780691141336 
|page= 64
}}</ref>
||[[File:Meissel–Mertens constant definition.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{M}</math>
||<math>\lim_{n \rightarrow \infty } \!\! \left( 
\sum_{p \leq n} \frac{1}{p} \! - \ln(\ln(n))\! \right) \!\! =
\underset{\!\!\!\! \gamma: \, \text{Euler constant} ,\,\, 
p: \, \text{prime}}{\! \gamma \! + \!\! \sum_{p} \!\left( \! 
\ln \! \left( \! 1 \! - \! \frac{1}{p} \! \right)
 \!\! + \! \frac{1}{p} \! \right)}</math>
||gamma+ <br> Sum[n=1 to ∞] <br> {ln(1-1/prime(n)) <br> +1/prime(n)}
|style="text-align:center;"|'''''[[Transcendental number|T]]''''' ?
||{{OEIS2C|A077761}}
||[0;3,1,4,1,2,5,2,1,1,1,1,13,4,2,4,2,1,33,296,...]
||1866 <br> & <br> 1873
||<small> 0.26149721284764278375542683860869585 </small>
|-

<!------------------------------------------v------------------------------------------->
|4.81047 73809 65351 65547
||John constant <ref>{{cite book 
|author= Steven R. Finch 
|title= Mathematical Constants
|url= http://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA466&lpg=PA466&dq=4.810477#v=onepage&q=4.810477&f=false
|year= 2003 
|publisher= Cambridge University Press
|isbn= 3-540-67695-3
|page= 466
}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math> \gamma </math>
||<math>\sqrt[i]{i} = i^{-i} = (i^i)^{-1} = (((i)^i)^i)^i = e^{\frac{\pi}{2}} = \sqrt{\sum_{n=0}^\infty \frac{\pi^{n}}{n!}}</math>
||e^(π/2)
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A042972}}
||[4;1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,3,2,...]
||
||<small> 4.81047738096535165547303566670383313 </small>
|-

<!-----------------------------------------v-------------------------------------------->
| -0.5 <br/> ± 0.86602 54037 84438 64676 '''''i'''''
||[[Cube Root]] of 1 <ref>{{cite book
|author= James Stuart Tanton
|title= Encyclopedia of Mathematics
|page= 458
|year= 2007
|publisher= 
|isbn= 0-8160-5124-0
|url= http://books.google.com/?id=MfKKMSuthacC&pg=PA358&dq=%22Root+of+unity%22#v=onepage&q=%22Root%20of%20unity%22&f=false
}}</ref>
||[[File:3rd roots of unity.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>\sqrt[3]{1}</math>
||<math> \begin{cases} \ \ 1 \\ -\frac{1}{2}+\frac{\sqrt{3}}{2}i \\ -\frac{1}{2}-\frac{\sqrt{3}}{2}i. \end{cases} </math>
||1, <br/> E^(2i pi/3), <br/> E^(-2i pi/3)
|style="text-align:center;"|'''''[[Complex number|C]]'''''
||{{OEIS2C|A010527}}
||- [0,5] <br> ± [0;1,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,...] i <br> - [0,5] <br> ± [0; 1, {{overline|6, 2}}] i
||
||<small> - 0.5 <br/> ± 0.8660254037844386467637231707529 '''''i''''' </small> 
|-

<!---------------------------------------------v---------------------------------------->
|<small> 0.11000 10000 00000 00000 0001 </small> <ref group=Mw>{{MathWorld|LiouvillesConstant|Liouville's Constant}}</ref>
||[[Liouville number]] <ref>{{cite book 
|author= Calvin C. Clawson
|title= Mathematical Traveler: Exploring the Grand History of Numbers
|url= http://books.google.com/?id=E3Eu3sV_anUC&pg=PA187&dq=Liouville+number+0.11000100000000000000000100#v=onepage&q=Liouville%20number%200.11000100000000000000000100&f=false
|year= 2003 
|publisher= Perseus
|isbn= 0-7382-0835-3
|page= 187 
}}</ref>
||<br><br><br>
|bgcolor=#e0f0f0 align=center|<math>\text{£}_{Li}</math>
||<math> \sum_{n=1}^\infty \frac{1}{10^{n!}} = \frac {1}{10^{1!}} + \frac{1}{10^{2!}} + \frac{1}{10^{3!}} + \frac{1}{10^{4!}}  + \cdots</math>
||Sum[n=1 to ∞] <br/> {10^(-n!)}
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A012245}}
||[1;9,1,999,10,9999999999999,1,9,999,1,9]
||
||<small> 0.11000100000000000000000100... </small>
|-

<!-----------------------------------------v-------------------------------------------->
|0.06598 80358 45312 53707 <ref group=Mw>{{MathWorld|PowerTower|Power Tower}}</ref>
||Lower limit of [[Tetration]] <ref>{{cite book 
|author= Jonathan Sondowa, Diego Marques
|title= Algebraic and transcendental solutions of some exponential equations
|url= http://ami.ektf.hu/uploads/papers/finalpdf/AMI_37_from151to164.pdf
|year= 2010
|publisher= Annales Mathematicae et Informaticae
|isbn= 
|page= 
}}</ref>
||[[File:Infinite power tower.svg|80px]]
|bgcolor=#e0f0f0 align=center|<math>{e}^{-e}</math>
||<math>\left(\frac {1}{e}\right)^e</math>
||1/(e^e)
||
||{{OEIS2C|A073230}}
||[0;15,6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1,...]
||
||<small> 0.06598803584531253707679018759684642 </small> 
|-

<!----------------------------------------v--------------------------------------------->
|1.83928 67552 14161 13255
||Tribonacci constant<ref>{{cite book
|author= T. Piezas.
|title= Tribonacci constant & Pi
|url= https://sites.google.com/site/tpiezas/0012
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math> {\phi_{}}_3 </math>
||<math>\textstyle \frac{1+\sqrt[3]{19+3\sqrt{33}}+\sqrt[3]{19-3\sqrt{33}}}{3} = \scriptstyle \, 1+ \left(\sqrt[3]{\tfrac12 + \sqrt[3]{\tfrac12 + \sqrt[3]{\tfrac12 + ...}}}\right)^{-1}</math>
||(1/3)*(1+(19+3 <br/> *sqrt(33))^(1/3) <br/> +(19-3 <br/> *sqrt(33))^(1/3))
<!--- 1+1/(((((((1/2)^(1/3)+1/2)^(1/3)+1/2)^(1/3)+1/2)^(1/3)+1/2)^(1/3)+1/2)^(1/3)) --->
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||{{OEIS2C|A058265}}
||[1;1,5,4,2,305,1,8,2,1,4,6,14,3,1,13,5,1,7,...]
||
||<small> 1.83928675521416113255185256465328660 </small>
|-

<!--------------------------------------------v----------------------------------------->
|0.36651 29205 81664 32701
||Median of the [[Gumbel distribution]] <ref>{{cite book
|author= Steven Finch
|title= Addenda to Mathematical Constants
|url= http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf
}}</ref>
||[[File:GumbelDichteF.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{ll_2}</math>
||<math>-\ln(\ln(2)) </math>
||-ln(ln(2))
||
||[http://oeis.org/A074785 A074785]
||[0;2,1,2,1,2,6,1,6,6,2,2,2,1,12,1,8,1,1,3,1,...]
||
||<small> 0.36651292058166432701243915823266947 </small>
|-

<!----------------------------------------------v--------------------------------------->
|36.46215 96072 07911 7709
||Pi^pi <ref>{{cite book 
|author= Renzo Sprugnoli.
|title= Introduzione alla Matematica
|url= http://www.dsi.unifi.it/~resp/media.pdf 
|year=  
|publisher= 
|isbn= 
|page= 
}}</ref>
||<br><br>
|bgcolor=#e0f0f0 align=center|<math>\pi ^\pi</math>
||<math>\pi ^\pi</math>
||pi^pi
||
||{{OEIS2C|A073233}}
||[36;2,6,9,2,1,2,5,1,1,6,2,1,291,1,38,50,1,2,...]
||
||<small> 36.4621596072079117709908260226921236 </small>
|-

<!---------------------------------------------v---------------------------------------->
|0.53964 54911 90413 18711
||Ioachimescu constant <ref>{{cite book 
|author= Chao-Ping Chen
|title= Ioachimescu's constant
|url= http://ajmaa.org/RGMIA/papers/v13n1/chen.pdf
|year=  
|publisher= 
|isbn= 
|page= 
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>2+\zeta(\tfrac12)</math>
||<math>{2{-}(1{+}\sqrt{2})\sum_{n=1}^\infty \frac{(-1)^{n+1}}{\sqrt{n}}} = \gamma + \sum_{n=1}^\infty \frac{(-1)^{2n} \; \gamma_n}{2^n n!} </math>
||''γ'' +N[<br/>sum[n=1 to ∞] <br/> {((-1)^(2n) <br/> gamma_n)<br/>/(2^n n!)}]
||
||2-<br/>{{OEIS2C|A059750}}
||[0;1,1,5,1,4,6,1,1,2,6,1,1,2,1,1,1,37,3,2,1,...]
||
||<small> 0.53964549119041318711050084748470198 </small>
|-

<!-----------------------------------------v-------------------------------------------->
|15.15426 22414 79264 1897 <ref group=Mw>{{MathWorld|PowerTower|Power Tower}}</ref>
||[[Escaping set|Exponential reiterated constant]] <ref>{{cite book 
|author= R. A. Knoebel.
|title= Exponentials Reiterated
|url= http://www.maa.org/sites/default/files/pdf/upload_library/22/Chauvenet/Knoebelchv.pdf
|year=  
|publisher= Maa.org
|isbn= 
|page= 
}}</ref>
||[[File:Exp-esc.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>e^e</math>
||<math> \sum_{n=0}^\infty \frac{e^n}{n!} = \lim_{n \to \infty} \left(\frac {1+n}{n} \right)^{n^{-n}(1+n)^{1+n}} </math>
||Sum[n=0 to ∞]<br/>{(e^n)/n!}
||
||{{OEIS2C|A073226}}
||[15;6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1,6,7,...]
||
||<small> 15.1542622414792641897604302726299119 </small>
|-

<!-------------------------------------------v------------------------------------------>
|0.64624 54398 94813 30426 <ref group=Mw>{{MathWorld|Masser-GramainConstant|Masser-Gramain Constant}}</ref>
||Masser–Gramain constant <ref>{{cite book 
|author= Eric W. Weisstein 
|title= CRC Concise Encyclopedia of Mathematics, Second Edition
|url= http://books.google.com/?id=aFDWuZZslUUC&pg=PA1861&lpg=PA1861&dq=masser+gramain+constant#v=onepage&q=masser%20gramain%20constant&f=false
|year= 2003 
|publisher= CRC Press
|isbn= 1-58488-347-2
|page= 1688
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{C}</math>
||<math> \gamma {\beta}(1) \! + \! {\beta}'(1) \! = \pi \! \left(-\!\ln \Gamma(\tfrac14)+\tfrac34 \pi+\tfrac12 \ln 2+\tfrac12 \gamma \right) </math>
<math> = \pi \! \left(-\!\ln (\tfrac14 !)+\tfrac34 \ln \pi -\tfrac32 \ln 2+\tfrac12 \, \gamma \right) </math> <math>\scriptstyle \gamma = \text{Euler–Mascheroni constant}= 0.5772156649\ldots</math>
<math>\scriptstyle \beta() = \text{Beta function} , \quad \scriptstyle \Gamma() = \text{Gamma function}</math>
||<small> Pi/4*(2*Gamma <br/>+ 2*Log[2]<br/> + 3*Log[Pi]- 4 <br/> Log[Gamma[1/4]]) </small>
||
||{{OEIS2C|A086057}}
||[0;1,1,1,4,1,3,2,3,9,1,33,1,4,3,3,5,3,1,3,4,...]
||
||<small> 0.64624543989481330426647339684579279 </small>
|-

<!------------------------------------------v------------------------------------------->
|1.11072 07345 39591 56175 <ref group=Mw>{{MathWorld|Bifoliate|Bifoliate}}</ref>
||The ratio of a square and circle circumscribed <ref>{{cite book 
|author= Richard J.Mathar.
|title= Table of Dirichlet L-series and Prime Zeta
|url= http://arxiv.org/pdf/1008.2547v1.pdf
|year=  
|publisher= Arxiv
|isbn= 
|page= 
}}</ref>
||[[File:Circumscribed2.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>\frac{\pi}{2\sqrt 2}</math>
||<math>\sum_{n = 1}^\infty \frac{({-}1)^{\lfloor \frac{n-1}{2}\rfloor}}{2n+1} = \frac{1}{1} + \frac{1}{3} - \frac{1}{5} - \frac{1}{7} + \frac{1}{9} + \frac{1}{11} - {\cdots}</math>
||sum[n=1 to ∞]<br/>{(-1)^(floor(<br/>(n-1)/2))<br/>/(2n-1)}
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A093954}}
||[1;9,31,1,1,17,2,3,3,2,3,1,1,2,2,1,4,9,1,3,...]
||
||<small> 1.11072073453959156175397024751517342 </small> 
|-

<!----------------------------------------------v--------------------------------------->
|1.45607 49485 82689 67139 <ref group=Mw>{{MathWorld|BackhousesConstant|Backhouse's Constant}}</ref>
||[[Backhouse's constant]] <ref>{{cite book 
|author= Eric W. Weisstein
|title= CRC Concise Encyclopedia of Mathematics, Second Edition
|url= http://books.google.com/?id=aFDWuZZslUUC&pg=PA151&dq=Backhouse+constant#v=onepage&q=%22Backhouse%20constant%22&f=false
|year= 2003 
|publisher= CRC Press
|isbn= 1-58488-347-2
|page= 151
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{B}</math>
||<math>\lim_{k \to \infty}\left | \frac{q_{k+1}}{q_k} \right \vert  \quad \scriptstyle \text {where:} \displaystyle \;\; Q(x)=\frac{1}{P(x)}= \! \sum_{k=1}^\infty q_k x^k  </math>
<math> P(x) =  \sum_{k=1}^\infty \underset{p_k\text{ prime}}{p_k x^k} = 1+2x+3x^2+5x^3+\cdots</math>
||1/( FindRoot[0 == 1 + Sum[x^n Prime[n], {n, 10000}], {x, {1}})
||
||{{OEIS2C|A072508}}
||[1;2,5,5,4,1,1,18,1,1,1,1,1,2,13,3,1,2,4,16,...]
||1995
||<small> 1.45607494858268967139959535111654355 </small>
|-

<!--------------------------------------------v----------------------------------------->
|1.85193 70519 82466 17036 <ref group=Mw>{{MathWorld|Wilbraham-GibbsConstant|Wilbraham-Gibbs Constant}}</ref>
||Gibbs constant <ref>{{cite book 
|author= Dave Benson
|title= Music: A Mathematical Offering
|url= http://books.google.com/?id=Ko1NsIq4qLIC&pg=PA53&dq=1.8519370#v=onepage&q=1.8519370&f=false
|year= 2006 
|publisher= Cambridge University Press
|isbn= 978-0-521-85387-3 
|page= 53
}}</ref>
||[[File:Sine integral.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{Si(\pi)}</math> <br/> [[Sin integral]]
||<math> \int_0^{\pi} \frac {\sin t}{t}\, dt =
\sum \limits_{n=1}^\infty (-1)^{n-1} \frac{\pi^{2n-1}}{(2n-1)(2n-1)!} </math> <br/>
<math> =  \pi- \frac{\pi^3}{3\cdot3!} + \frac{\pi^5}{5\cdot5!} - \frac{\pi^7}{7\cdot7!} + \cdots  </math>
||SinIntegral[Pi]
||
||{{OEIS2C|A036792}}
||[1;1,5,1,3,15,1,5,3,2,7,2,1,62,1,3,110,1,39,...]
||
||<small> 1.85193705198246617036105337015799136 </small> 
|-

<!--------------------------------------------v----------------------------------------->
|0.23571 11317 19232 93137 <ref group=Mw>{{MathWorld|Copeland-ErdosConstant|Copeland-Erdos Constant}}</ref>
||[[Copeland–Erdős constant]] <ref>{{cite book 
|author= Yann Bugeaud 
|title= Distribution Modulo One and Diophantine Approximation
|url= http://books.google.com/?id=NeEpoAf7k0IC&pg=PA87&dq=0.235711131719232931#v=onepage&q=0.235711131719232931&f=false
|year=  2012
|publisher= Cambridge University Press
|isbn=978-0-521-11169-0
|page= 87
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{\mathcal{C}_{CE}}</math>
||<math>\sum _{n=1}^\infty \frac{p_n} {10^{n + \sum \limits_{k=1}^n \lfloor \log_{10}{p_k} \rfloor }}</math> 
||<small> sum[n=1 to ∞] <br/> {prime(n) /(n+(10^ <br/> sum[k=1 to n]{floor <br/> (log_10 prime(k))}))} </small>
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||{{OEIS2C|A033308}}
||[0;4,4,8,16,18,5,1,1,1,1,7,1,1,6,2,9,58,1,3,...]
||
||<small> 0.23571113171923293137414347535961677 </small>
|-

<!-----------------------------------------v-------------------------------------------->
|1.52362 70862 02492 10627 <ref group=Mw>{{MathWorld|DragonCurve|Dragon Curve}}</ref>
||Fractal dimension of the boundary of the [[dragon curve]] <ref>{{cite book 
|author= Angel Chang y Tianrong Zhang
|title= On the Fractal Structure of the Boundary of Dragon Curve
|url= http://poignance.coiraweb.com/math/Fractals/Dragon/Bound.html
|year=  
|publisher= 
|isbn= 
|page= 
}}</ref>
||[[File:Fractal dragon curve.jpg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{C_d}</math>
||<math>\frac{\log\left(\frac{1+\sqrt[3]{73-6\sqrt{87}}+\sqrt[3]{73+6\sqrt{87}}}{3}\right)}
{\log(2)}</math>
||(log((1+(73-6 sqrt(87))^1/3+ (73+6 sqrt(87))^1/3)<br/>/3))/ log(2)))
||
||
||[1;1,1,10,12,2,1,149,1,1,1,3,11,1,3,17,4,1,...]
||
||<small> 1.52362708620249210627768393595421662 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|1.78221 39781 91369 11177 <ref group=Mw>{{MathWorld|GrothendiecksConstant|Grothendieck's Constant}}</ref>
||Grothendieck constant <ref>{{cite book 
|author= Joe Diestel
|title= Absolutely Summing Operators
|url= http://books.google.com/?id=pHqyRSdgVTsC&pg=PA29&lpg=PA29&dq=1.782+GROTHENDIECK#v=onepage&q=1.782%20GROTHENDIECK&f=false
|year= 1995 
|publisher= Cambridge University Press
|isbn= 0-521-43168-9
|page= 29
}}</ref>
||<br><br><br>
|bgcolor=#e0f0f0 align=center|<math>{K_{R}}</math>
||<math> \frac {\pi}{2 \log(1+\sqrt{2})} </math>
||pi/(2 log(1+sqrt(2)))
||
||{{OEIS2C|A088367}}
||[1;1,3,1,1,2,4,2,1,1,17,1,12,4,3,5,10,1,1,3,...]
||
||<small> 1.78221397819136911177441345297254934 </small> 
|-

<!---------------------------------------------v---------------------------------------->
|1.58496 25007 21156 18145 <ref group=Mw>{{MathWorld|PascalsTriangle|Pascal's Triangle}}</ref>
||[[Hausdorff dimension]], [[Sierpinski triangle]] <ref>{{cite book 
|author= Eric W. Weisstein
|title= CRC Concise Encyclopedia of Mathematics, Second Edition
|url= http://books.google.com/?id=aFDWuZZslUUC&pg=PA2685&dq=1.584962500#v=onepage&q=1.584962500&f=false
|year= 2002  
|publisher= CRC Press
|isbn= 1-58488-347-2
|page= 1356
}}</ref>
||[[File:SierpinskiTriangle-ani-0-7.gif|100px]]
|bgcolor=#e0f0f0 align=center|<math>{log_2 3}</math>
||<math>\frac {\log 3}{\log 2} = \frac{\sum_{n=0}^\infty \frac{1}{2^{2n+1}(2n+1)}}{\sum_{n=0}^\infty \frac{1}{3^{2n+1}(2n+1)}} = \frac{\frac{1}{2}+\frac{1}{24}+\frac{1}{160}+\cdots}{\frac{1}{3}+\frac{1}{81}+\frac{1}{1215}+\cdots} </math>
||<small>( Sum[n=0 to ∞] {1/<br/>(2^(2n+1) (2n+1))})/ <br/> (Sum[n=0 to ∞] {1/<br/>(3^(2n+1) (2n+1))})</small>
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A020857}}
||[1;1,1,2,2,3,1,5,2,23,2,2,1,1,55,1,4,3,1,1,...]
||
||<small> 1.58496250072115618145373894394781651 </small>  
|-

<!-------------------------------------------v------------------------------------------>
|1.30637 78838 63080 69046 <ref group=Mw>{{MathWorld|MillsConstant|Mills Constant}}</ref>
||[[Mills' constant]] <ref>{{cite book 
|author= Laith Saadi 
|title= Stealth Ciphers
|url= http://books.google.com/?id=Mll0WZAjdyEC&pg=PT170&dq=%22Mills%27+constant%22#v=onepage&q=%22Mills%27%20constant%22&f=false
|year= 2004
|publisher= Trafford Publishing 
|isbn= 978-1-4120-2409-9
|page= 160
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{\theta}</math>
||<math> \lfloor A^{3^{n}} \rfloor</math>
||Nest[ NextPrime[#^3] &, 2, 7]^(1/3^8)
||
||{{OEIS2C|A051021}}
||[1;3,3,1,3,1,2,1,2,1,4,2,35,21,1,4,4,1,1,3,2,...]
||1947
||<small> 1.30637788386308069046861449260260571 </small> 
|-

<!----------------------------------------v--------------------------------------------->
|2.02988 32128 19307 25004 <ref group=Mw>{{MathWorld|FigureEightKnot|Figure Eight Knot}}</ref>
||Figure eight knot hyperbolic volume <ref>{{cite book 
|author= Jonathan Borwein,David Bailey
|title= Mathematics by Experiment, 2nd Edition: Plausible Reasoning in the 21st Century
|url= http://books.google.com/?id=ysDiE0Enn4oC&pg=PA56&lpg=PA56&dq=2.029883212819307250042405108549#v=onepage&q=2.029883212819307250042405108549&f=false
|year= 2008
|publisher= A K Peters, Ltd.
|isbn= 978-1-56881-442-1
|page= 56
}}</ref>
||[[File:Blue Figure-Eight Knot.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>{V_{8}}</math>
||<math> 2 \sqrt{3}\, \sum_{n=1}^\infty \frac{1}{n
{2n \choose n}} \sum_{k=n}^{2n-1} \frac{1}{k} = 
6 \int \limits_{0}^{\pi / 3} 
\log \left( \frac{1}{2 \sin t} \right) \, dt = </math> 
<math>\scriptstyle
\frac{\sqrt{3}}{{9}}\, \sum \limits_{n=0}^\infty 
\frac{(-1)^n}{27^n}\,\left\{\!
\frac{{18}}{(6n+1)^2} - \frac{{18}}{(6n+2)^2} -
\frac{{24}}{(6n+3)^2} -
\frac{{6}}{(6n+4)^2} +
\frac{{2}}{(6n+5)^2}\!\right\}
</math>
||6 integral[0 to pi/3]<br/> {log(1/(2 sin (n)))}
||
||{{OEIS2C|A091518}}
||[2;33,2,6,2,1,2,2,5,1,1,7,1,1,1,113,1,4,5,1,...]
||
||<small> 2.02988321281930725004240510854904057 </small> 
|-

<!------------------------------------------v------------------------------------------->
|262 53741 26407 68743 <br> .99999 99999 99250 073 <ref group=Mw>{{MathWorld|RamanujanConstant|Ramanujan Constant}}</ref>
||[[Complex multiplication|Hermite–Ramanujan constant]]<ref>{{cite book 
|author= L. J. Lloyd James Peter Kilford 
|title= Modular Forms: A Classical and Computational Introduction
|url= http://books.google.com/?id=txPhITLO1YoC&pg=PA107&dq=262537412640768743.99999999999925#v=onepage&q=262537412640768743.99999999999925&f=false
|year= 2008  
|publisher= Imperial College Press
|isbn= 978-1-84816-213-6
|page= 107
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{R}</math> 
||<math> e^{\pi\sqrt{163}}</math>
||e^(π sqrt(163))
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A060295}}
||<small>[262537412640768743;1,1333462407511,1,8,1,1,5,...]</small>
||1859
||<small> 262537412640768743.999999999999250073 </small> 
|-

<!---------------------------------------------v---------------------------------------->
|1.74540 56624 07346 86349 <ref group=Mw>{{MathWorld|KhinchinHarmonicMean|KhinchinHarmonicMean}}</ref>
||Khinchin [[harmonic mean]] <ref>{{cite book 
|author= 
|title= Continued Fractions from Euclid till Present
|url= http://algo.inria.fr/seminars/sem98-99/vardi1-2.html#Finch95b
|year=  1998
|publisher= IHES, Bures sur Yvette
|isbn= 
|page= 
}}</ref>
||[[File:Plot harmonic mean.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>{K_{-1}}</math>
||<math> \frac {\log 2} {\sum \limits_{n=1}^\infty \frac {1}{n}
 \log\bigl(1{+}\frac{1}{n(n+2)}\bigr)} = \lim_{n \to \infty} \frac{n}{\frac{1}{a_1}+\frac{1}{a_2}+\cdots+\frac{1}{a_n}}</math>
''a''<sub>1</sub> ... ''a''<sub>''n''</sub> are elements of a [[continued fraction]] [''a''<sub>0</sub>; ''a''<sub>1</sub>, ''a''<sub>2</sub>, ..., ''a''<sub>''n''</sub>]
||(log 2)/<br/>(sum[n=1 to ∞] <br/>{1/n log(1+<br/>1/(n(n+2))}
||
||{{OEIS2C|A087491}}
||[1;1,2,1,12,1,5,1,5,13,2,13,2,1,9,1,6,1,3,1,...]
||
||<small> 1.74540566240734686349459630968366106 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|1.64872 12707 00128 14684 <ref group=Ow>[http://oeis.org/wiki/Sqrt(e) Sqrt(e)]</ref>
||[[Square root]] of the [[number e]] <ref>{{cite book 
|author= Julian Havil
|title= The Irrationals: A Story of the Numbers You Can't Count On
|url= http://books.google.com/?id=BoqXQ87C-04C&pg=PA98&dq=1.6487212707#v=onepage&q=1.6487212707&f=false 
|year= 2012
|publisher= Princeton University Press
|isbn= 978-0-691-14342-2
|page= 98
}}</ref>
||<br><br><br>
|bgcolor=#e0f0f0 align=center|<math>\sqrt {e}</math>
||<math>\sum_{n = 0}^\infty \frac{1}{2^n n!} = \sum_{n = 0}^\infty \frac{1}{(2n)!!} = \frac{1}{1}+\frac{1}{2}+\frac{1}{8}+\frac{1}{48}+\cdots</math>
||Sum[n=0 to ∞]<br/>{1/(2^n n!)}
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A019774}}
||[1;1,1,1,5,1,1,9,1,1,13,1,1,17,1,1,21,1,1,...] <br> = [1;1,{{overline|1,1,4p+1}}],  p∈ℕ
||
||<small> 1.64872127070012814684865078781416357 </small>
|-

<!--------------------------------------------v----------------------------------------->
|1.01734 30619 84449 13971 <ref group=Mw>{{MathWorld|RiemannZetaConstant|Riemann Zeta Constant}}</ref>
||Zeta(6) <ref>{{cite book 
|author=  Lennart R©Æde,Bertil Westergren 
|title= Mathematics Handbook for Science and Engineering
|url= 
|year= 2004
|publisher= Springer-Verlag 
|isbn= 3-540-21141-1
|page= 194
}}</ref>
||[[File:Zeta.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>\zeta(6)</math>
||<math>\frac{\pi^6}{945} \! = \! \prod_{n=1}^\infty \! \underset{p_n: \text{ prime}}{ \frac{1}{{1-p_n}^{-6}}} = \frac{1}{1 \! -\! 2^{-6}} \! \cdot \! \frac{1}{1 \! - \! 3^{-6}}  \! \cdot \! \frac{1}{1 \! - \! 5^{-6}} \cdots</math>
||Prod[n=1 to ∞]<br/>{1/(1-ithprime<br/>(n)^-6)} 
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A013664}}
||[1;57,1,1,1,15,1,6,3,61,1,5,3,1,6,1,3,3,6,1,...]
||
||<small> 1.01734306198444913971451792979092052 </small> 
|-

<!----------------------------------------v--------------------------------------------->
|0.10841 01512 23111 36151 <ref group=Mw>{{MathWorld|TrottConstant|Trott Constant}}</ref>
||Trott constant <ref>{{cite book 
|author=  Michael Trott
|title= Finding Trott Constants
|url= http://www.mathematica-journal.com/issue/v10i2/contents/Corner10-2/Corner10-2.pdf 
|year=  
|publisher= Wolfram Research
|isbn= 
|page= 
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>\mathrm{T}_1</math>
||<math> \textstyle [1, 0, 8, 4, 1, 0, 1, 5, 1, 2, 2, 3, 1, 1, 1, 3, 6,...]</math> <br/>
<math> \tfrac 1{1+\tfrac 1{0+\tfrac 1{8+\tfrac 1{4+\tfrac 1{1+\tfrac 1{0+1{/\cdots}}}}}}} </math>
||Trott Constant
||
||{{OEIS2C|A039662}}
||[0;9,4,2,5,1,2,2,3,1,1,1,3,6,1,5,1,1,2,...]
||
||<small> 0.10841015122311136151129081140641509</small> 
|-

<!------------------------------------------v------------------------------------------->
|0.00787 49969 97812 3844 <ref group=Mw>{{MathWorld|ChaitinsConstant|Chaitin's Constant}}</ref>
||[[Chaitin constant]] <ref>{{cite book 
|author= David Darling 
|title= The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes
|url= http://books.google.com/?id=HrOxRdtYYaMC&pg=PA63&dq=%22Chaitin+constant%22#v=onepage&q=%22Chaitin%20constant%22&f=false
|year= 2004
|publisher= Wiley & Sons inc.
|isbn= 0-471-27047-4
|page= 63
}}</ref>
||<center>[[File:ProgramTree.svg|40px]]</center>
|bgcolor=#e0f0f0 align=center|<math>\Omega </math>
||<center><math>\sum_{p \in P} 2^{-|p|} 
\overset {p: \text{ Halted program}}{
 \underset{ P:\text{ Domain of all programs that stop.}}
{\scriptstyle  {|p|}:\text{Size in bits of program }p}}</math>
<br>See also: [[Halting problem]]</center>
||
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A100264}}
||[0; 126, 1, 62, 5, 5, 3, 3, 21, 1, 4, 1]
||1975
||0.0078749969978123844 
|-

<!-----------------------------------------v-------------------------------------------->
|0.83462 68416 74073 18628 <ref group=Mw>{{MathWorld|GausssConstant|Gauss's Constant}}</ref>
||[[Gauss constant]] <ref>{{cite book 
|author= Keith B. Oldham,Jan C. Myland,Jerome Spanier 
|title= An Atlas of Functions: With Equator, the Atlas Function Calculator
|url= http://books.google.com/?id=UrSnNeJW10YC&pg=PA647&dq=%22Gauss%27s+constant%22#v=onepage&q=%22atlas%20is%20the%20Gauss%27s%20constant%22&f=false
|year= 2009  
|publisher= Springer 
|isbn= 978-0-387-48806-6
|page= 15
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{G}</math>
|| <math>  \frac{1}{\mathrm{agm}(1, \sqrt{2})} = \frac{4 \sqrt{2} \,(\tfrac14 !)^2}{\pi ^{3/2}}= \frac{2}{\pi}\int_0^1\frac{dx}{\sqrt{1 - x^4}}</math>
AGM = [[Arithmetic–geometric mean]]
||(4 sqrt(2)((1/4)!)^2)<br/>/pi^(3/2)
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A014549}}
||[0;1,5,21,3,4,14,1,1,1,1,1,3,1,15,1,3,7,1,...]
||
||<small> 0.83462684167407318628142973279904680 </small> 
|-

<!---------------------------------------v---------------------------------------------->
|1.45136 92348 83381 05028 <ref group=Mw>{{MathWorld|SoldnersConstant|Soldner's Constant}}</ref>
||[[Ramanujan–Soldner constant]]<ref>{{cite book
|author= Johann Georg Soldner
|title= Théorie et tables d’une nouvelle fonction transcendante
|language= fr
|url= http://books.google.de/books?id=g4Q_AAAAcAAJ&pg=PA42
|year= 1809
|editor= Lindauer, München
|page= 42
}}</ref><ref>{{cite book
|author= Lorenzo Mascheroni
|title= Adnotationes ad calculum integralem Euleri
|language= latin
|url= http://books.google.com/books?id=XkgDAAAAQAAJ&hl=de&pg=RA1-PA17
|year= 1792
|editor= Petrus Galeatius, Ticini
|page= 17
}}</ref>
||[[File:Integrallogrithm.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>{\mu}</math>
||<math> \mathrm{li}(x) = \int\limits_0^x  \frac{dt}{\ln t} = 0  
{\color{White}{......}} </math>  li = [[Logarithmic integral]] <br/>
<math> \mathrm{li}(x)\;=\;\mathrm{Ei}(\ln{x})  
{\color{White}{........}} </math> Ei = [[Exponential integral]]
||FindRoot[li(x) = 0]
|style="text-align:center;"|'''''[[Irrational number|I]]'''''
||{{OEIS2C|A070769}}
||[1;2,4,1,1,1,3,1,1,1,2,47,2,4,1,12,1,1,2,2,1,...]
||1792 <br> to <br> 1809
||<small> 1.45136923488338105028396848589202744 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|0.64341 05462 88338 02618 <ref group=Mw>{{MathWorld|CahensConstant|Cahen's Constant}}</ref>
||[[Cahen's constant]] <ref>{{cite book 
|author= Yann Bugeaud
|title= Series representations for some mathematical constants
|url= http://books.google.com/?id=iAg8FL5jKSgC&pg=PA72&dq=%22cahen+constant%22#v=onepage&q=%22cahen%20constant%22&f=false
|year= 2004
|publisher= 
|isbn= 0-521-82329-3
|page= 72
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>\xi _{2}</math>
||<math> \sum_{k=1}^{\infty} \frac{(-1)^{k}}{s_k-1} = \frac{1}{1} - \frac{1}{2} + \frac{1}{6} - \frac{1}{42} + \frac{1}{1806} {\,\pm \cdots}  </math> 
<small> Where s<sub>k</sub> is the kth term of ''[[Sylvester's sequence]]'' 2, 3, 7, 43, 1807, ...</small>
<br/> Defined as:  <math>\, \, S_0= \, 2 , \,\, S_k= \, 1+\prod \limits_{n=0}^{k-1} S_n\text{ for}\;k>0 </math>
||
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A080130}}
||[0; 1, 1, 1, 4, 9, 196, 16641, 639988804, ...]
||1891
|<small> 0.64341054628833802618225430775756476 </small> 
|-

<!------------------------------------------v------------------------------------------->
|1.41421 35623 73095 04880 <ref group=Mw>{{MathWorld|PythagorassConstant|Pythagoras's Constant}}</ref>
||[[Square root of 2]], [[Pythagoras]] constant.<ref>{{cite book 
|author= Calvin C Clawson 
|title= Mathematical sorcery: revealing the secrets of numbers
|url= http://books.google.com/?id=sPRbZACsXogC&pg=PA293&dq=pi+nested+radical#v=snippet&q=%22Again%20we%20have%20an%20amazing%20expression.%22&f=false
|year=  2001
|publisher= 
|isbn= 978 0 7382 0496-3
|page= IV
}}</ref>
||[[File:Square root of 2 triangle.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>\sqrt{2}</math>
||<math>\! \prod_{n=1}^\infty \! \left( 1 \! + \! \frac{(-1)^{n+1}}{2n-1} \right) \! = \! \left(1 \! + \! \frac{1}{1}\right) \! \left(1 \! - \! \frac{1}{3} \right) \! \left(1 \! + \! \frac{1}{5} \right) \cdots </math>
||prod[n=1 to ∞] <br/> {1+(-1)^(n+1) <br/> /(2n-1)}
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||{{OEIS2C|A002193}}
||[1;2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,...]<br> = [1;{{overline|2}}...]
||
||<small> 1.41421356237309504880168872420969808 </small> 
|-

<!------------------------------------------v------------------------------------------->
|1.77245 38509 05516 02729 <ref group=Mw>{{MathWorld|Carlson-LevinConstant|Carlson-Levin Constant}}</ref>
||Carlson–Levin constant <ref>{{cite book 
|author= H.M. Antia
|title= Numerical Methods for Scientists and Engineers
|url= http://books.google.com/?id=YzXsZgjyFA4C&pg=PA220&dq=1.772453850905516#v=onepage&q=1.772453850905516&f=false
|year= 2000
|publisher= Birkhäuser Verlag
|isbn= 3-7643-6715-6
|page= 220
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{\Gamma}(\tfrac12)</math>
||<math>\sqrt{\pi} = \left(-\frac{1}{2}\right)! = \int_{-\infty }^{\infty } \frac {1}{e^{x^2}} \, dx  = \int_{0 }^{1} \frac {1}{\sqrt{-\ln x}} \, dx </math> 
||sqrt (pi)
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A002161}}
||[1;1,3,2,1,1,6,1,28,13,1,1,2,18,1,1,1,83,1,...]
||
||<small> 1.77245385090551602729816748334114518 </small> 
|-

<!--------------------------------------------v----------------------------------------->
|1.05946 30943 59295 26456 <ref group=Ow>[http://oeis.org/wiki/2#Roots_and_powers_of_2 Roots and powers of 2]</ref>
||Musical interval between each half tone <ref>{{cite book 
|author= Bart Snapp 
|title= Numbers and Algebra
|url= http://www.math.osu.edu/~snapp.14/1165/NumbersAlgebra.pdf
|year= 2012
}}</ref><ref>{{cite book 
|author= George Gheverghese Joseph 
|title= The Crest of the Peacock: Non-European Roots of Mathematics
|url= http://books.google.com/?id=ymud91nTc9YC&pg=PA295&dq=1.059463094359295264561825#v=onepage&q=1.059463094359295264561825&f=false
|year= 2011  
|publisher= Princeton University Press
|isbn= 978-0-691-13526-7
|page= 295
}}</ref>
||[[Image:Rast scale.svg|100px]]
[[Image:YB0214 Clavier tempere.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>\sqrt[12]{2}</math>
||<math> \scriptstyle 440\, Hz. \textstyle 2^\frac{1}{12} \, 2^\frac{2}{12} \, 2^\frac{3}{12} \, 2^\frac{4}{12} \, 2^\frac{5}{12} \, 2^\frac{6}{12} \, 2^\frac{7}{12} \, 2^\frac{8}{12} \, 2^\frac{9}{12} \, 2^\frac{10}{12} \, 2^\frac{11}{12} \, 2 </math> <br>
<math> \scriptstyle {\color{white}...\color{black} Do_1\;\;  Do\#\;\,  Re\;\,  Re\#\;\,  Mi\;\;  Fa\;\;  Fa\#\;  Sol\;\,  Sol\#\, La\;\;  La\#\;\;  Si\;\,  Do_2} </math>
<math> \scriptstyle {\color{white}....\color{black}C_1\;\;\;\;  C\#\;\;\;\,  D\;\;\;  D\#\;\;\,  E\;\;\;\;\,  F\;\;\;\,  F\#\;\;\;  G\;\;\;\;  G\#\;\;\;  A\;\;\;\,  A\#\;\;\;\,  B\;\;\;  C_2}  </math>
||2^(1/12)
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||{{OEIS2C|A010774}}
||[1;16,1,4,2,7,1,1,2,2,7,4,1,2,1,60,1,3,1,2,...]
||
||<small> 1.05946309435929526456182529494634170 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|1.01494 16064 09653 62502 <ref group=Mw>{{MathWorld|GiesekingsConstant|Gieseking's Constant}}</ref>
||[[:de:Gieseking-Konstante|Gieseking constant]] <ref>{{cite book 
|author= Steven Finch
|title= Volumes of Hyperbolic 3-Manifolds
|url= http://www.people.fas.harvard.edu/~sfinch/csolve/hyp.pdf
|year=  
|publisher= Harvard University
|isbn= 
|page= 
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{\pi \ln \beta} </math>
||<math>\frac{3\sqrt{3}}{4} \left(1- \sum_{n=0}^\infty \frac{1}{(3n+2)^2}+ \sum_{n=1}^\infty\frac{1}{(3n+1)^2} \right)= </math> <br/> 
<math>\textstyle \frac{3\sqrt{3}}{4} \left( 1 - \frac{1}{2^2} + \frac{1}{4^2}-\frac{1}{5^2}+\frac{1}{7^2}-\frac{1}{8^2}+\frac{1}{10^2} \pm \cdots \right)</math>.
||sqrt(3)*3/4 *(1<br/>-Sum[n=0 to ∞]<br/>{1/((3n+2)^2)}<br/>+Sum[n=1 to ∞]<br/>{1/((3n+1)^2)})
||
||{{OEIS2C|A143298}}
||[1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11,...]
||1912
||<small> 1.01494160640965362502120255427452028 </small> 
|-

<!---------------------------------------------v---------------------------------------->
|2.62205 75542 92119 81046 <ref group=Mw>{{MathWorld|LemniscateConstant|Lemniscate Constant}}</ref>
||[[Lemniscate constant]] <ref>{{cite book 
|author= J. Coates,Martin J. Taylor
|title= L-Functions and Arithmetic
|url= http://books.google.com/?id=aKQhpm1h770C&pg=PA333&dq=2.6220575#v=onepage&q&f=false
|year= 1991 
|publisher= Cambridge University Press
|isbn= 0-521-38619-5
|page= 333
}}</ref>
||[[File:Lemniscate of Gerono.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{\varpi} </math>
||<math> \pi \, {G} = 4 \sqrt{\tfrac2\pi}\,\Gamma{\left(\tfrac54 \right)^2} = \tfrac14 \sqrt{\tfrac{2}{\pi}}\,\Gamma {\left(\tfrac14 \right)^2} = 4 \sqrt{\tfrac2\pi}\left(\tfrac14 !\right)^2</math>
|| 4 sqrt(2/pi)<br/>((1/4)!)^2
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A062539}}
||[2;1,1,1,1,1,4,1,2,5,1,1,1,14,9,2,6,2,9,4,1,...]
||1798
||<small> 2.62205755429211981046483958989111941 </small> 
|-

<!---------------------------------------------v---------------------------------------->
|1.28242 71291 00622 63687 <ref group=Mw>{{MathWorld|Glaisher-KinkelinConstant|Glaisher-Kinkelin Constant}}</ref>
||[[Glaisher–Kinkelin constant]] <ref>{{cite book 
|author= Jan Feliksiak 
|title= The Symphony of Primes, Distribution of Primes and Riemann’s Hypothesis
|url= http://books.google.com/?id=HFlgz7JoS-MC&pg=PA18&dq=Glaisher%E2%80%93Kinkelin+constant#v=onepage&q=Glaisher%E2%80%93Kinkelin&f=false
|year=  2013
|publisher= Xlibris Corporation
|isbn= 978-1-4797-6558-4
|page= 18
}}</ref>
||<br><br><br>
|bgcolor=#e0f0f0 align=center|<math>{A}</math>
||<math> e^{\frac{1}{12}-\zeta^\prime(-1)} =
 e^{\frac{1}{8}-\frac{1}{2}\sum\limits_{n=0}^\infty \frac{1}{n+1} \sum\limits_{k=0}^n \left(-1\right)^k \binom{n}{k} \left(k+1\right)^2 \ln(k+1)}</math>
||e^(1/12-zeta´{-1})
|style="text-align:center;"|'''''[[Transcendental number|T]]''''' ?
||{{OEIS2C|A074962}}
||[1;3,1,1,5,1,1,1,3,12,4,1,271,1,1,2,7,1,35,...]
||
||<small> 1.28242712910062263687534256886979172 </small> 
|-

<!------------------------------------------v------------------------------------------->
| -4.22745 35333 76265 408 <ref group=Mw>{{MathWorld|GausssDigammaTheorem|Gausss Digamma Theorem}}</ref>
||[[Digamma function|Digamma]] (1/4) <ref>{{cite book 
|author= Horst Alzera, Dimitri Karayannakisb, H.M. Srivastava 
|title= Series representations for some mathematical constants
|url= http://www.sciencedirect.com/science/article/pii/S0022247X05005883
|year=  2005
|publisher= Elsevier Inc 
|isbn= 
|page= 149
}}</ref>
||[[File:Complex Polygamma 0.jpg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{\psi} (\tfrac14) </math>
|| <math>  -\gamma -\frac{\pi}{2} - 3\ln{2} = -\gamma+\sum_{n=0}^{\infty}\left(\frac{1}{n+1}-\frac{1}{n+\tfrac14}\right)</math>
||-EulerGamma <br/>-\pi/2 -3 log 2
||
||{{OEIS2C|A020777}}
||-[4;4,2,1,1,10,1,5,9,11,1,22,1,1,14,1,2,1,4,...]
||
||<small> -4.2274535333762654080895301460966835 </small> 
|-

<!------------------------------------------v------------------------------------------->
|0.28674 74284 34478 73410 <ref group=Mw>{{MathWorld|CarefreeCouple|Carefree Couple}}</ref>
||Strongly Carefree constant <ref>{{cite book 
|author= Steven R. Finch 
|title= Quadratic Dirichlet L-Series
|url= http://www.people.fas.harvard.edu/~sfinch/csolve/ls.pdf
|year= 2005 
|publisher= 
|isbn= 
|page= 12
}}</ref>
||<br><br><br><br>
|bgcolor=#e0f0f0 align=center|<math>K_{2}</math>
||<math> \prod_{n=1}^\infty \underset{p_n: \text{ prime}} {\left( 1-\frac{3 p_n-2}{{p_n}^{3}}\right)} = \frac {6}{\pi ^2}\prod_{n=1}^\infty \underset{p_n: \text{ prime}} {\left( 1-\frac{1}{{p_n(p_n+1)}}\right)} </math> 
||<small> N[ prod[k=1 to ∞] <br/> {1-(3*prime(k)-2) <br/> /(prime(k)^3)}] </small>
||
||{{OEIS2C|A065473}}
||[0;3,2,19,3,12,1,5,1,5,1,5,2,1,1,1,1,1,3,7,...]
||
||<small> 0.28674742843447873410789271278983845  </small> 
|-

<!---------------------------------------------v---------------------------------------->
|1.78107 24179 90197 98523 <ref group=Mw>{{MathWorld|Euler-MascheroniConstant|Euler-Mascheroni Constant}}</ref>
||Exp.gamma, <br/> [[Barnes G-function]] <ref>{{cite book 
|author= H. M. Srivastava,Junesang Choi 
|title= Zeta and q-Zeta Functions and Associated Series and Integrals
|url= http://books.google.com/?id=DUyACqwqaqIC&pg=PA613&dq=%22Barnes+G-Function%22#v=onepage&q=%22generalized%20Barnes%20G-function%22&f=false
|year= 2012  
|publisher= Elsevier
|isbn= 978-0-12-385218-2
|page= 613
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>e^{\gamma} </math>
||<math>\prod_{n=1}^\infty \frac{e^{\frac{1}{n}}}{1+\tfrac1n} = \prod_{n=0}^\infty \left(\prod_{k=0}^n (k+1)^{(-1)^{k+1}{n \choose k}}\right)^{\frac{1}{n+1}} = </math>
<math>\textstyle \left ( \frac{2}{1} \right )^{1/2} \left (\frac{2^2}{1 \cdot 3} \right )^{1/3} \left (\frac{2^3 \cdot 4}{1 \cdot 3^3} \right )^{1/4}
\left (\frac{2^4 \cdot 4^4}{1 \cdot 3^6 \cdot 5} \right )^{1/5}\cdots </math>
||Prod[n=1 to ∞]<br/>{e^(1/n)}<br/>/{1 + 1/n}
||
||{{OEIS2C|A073004}}
||[1;1,3,1,1,3,5,4,1,1,2,2,1,7,9,1,16,1,1,1,2,...]
||
||<small> 1.78107241799019798523650410310717954 </small> 
|-

<!----------------------------------------v--------------------------------------------->
|3.62560 99082 21908 31193 <ref group=Mw>{{MathWorld|GammaFunction|Gamma Function}}</ref>
||Gamma(1/4)<ref>{{cite book 
|author= Refaat El Attar 
|title= Special Functions And Orthogonal Polynomials
|url= http://books.google.com/?id=r3Zj__Ag7LwC&pg=PA58&dq=3.6256#v=onepage&q=3.6256&f=false
|year= 2006 
|publisher= Lulu Press
|isbn= 1-4116-6690-9
|page= 58
}}</ref>
||[[File:Gamma abs 3D.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>\Gamma(\tfrac14)</math>
||<math> 4 \left(\frac{1}{4}\right)! = \left(-\frac{3}{4}\right)! </math>
||4(1/4)!
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A068466}}
||[3;1,1,1,2,25,4,9,1,1,8,4,1,6,1,1,19,1,1,4,1,...]
||1729
||<small> 3.62560990822190831193068515586767200 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|1.66168 79496 33594 12129 <ref group=Mw>{{MathWorld|SomossQuadraticRecurrenceConstant|SomossQuadraticRecurrence Constant}}</ref>
||[[Somos' quadratic recurrence constant]] <ref>{{cite book
|author= Jesus Guillera and Jonathan Sondow
|title= Double integrals and infinite products...
|editor= arxiv.org
|url= http://arxiv.org/pdf/math/0506319v3.pdf
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{\sigma}</math>
||<math>\prod_{n=1}^\infty n^{{1/2}^n} = \sqrt {1 \sqrt {2 \sqrt{3 \cdots}}} = 1^{1/2} \; 2^{1/4} \; 3^{1/8} \cdots </math> 
||prod[n=1 to ∞]<br/>{n ^(1/2)^n}
|style="text-align:center;"|'''''[[Transcendental number|T]]''''' ?
||{{OEIS2C|A065481}}
||[1;1,1,1,21,1,1,1,6,4,2,1,1,2,1,3,1,13,13,...]
||
||<small> 1.66168794963359412129581892274995074 </small> 
|-

<!-----------------------------------------v-------------------------------------------->
|0.95531 66181 245092 78163
||[[Magic angle]] <ref>{{cite book 
|author= Andras Bezdek
|title= Discrete Geometry
|url= http://books.google.com/?id=WoaxgpHu19gC&pg=PA150&lpg=PA150&dq=0.955316#v=onepage&q=0.955316&f=false
|year= 2003
|publisher= Marcel Dekkcr, Inc.
|isbn= 0-8247-0968-3
|page= 150
}}</ref>
||[[File:Magic angle.png|100px]]
|bgcolor=#e0f0f0 align=center|<math> {\theta_m} </math>
||<math> \arctan \left(\sqrt{2}\right) = \arccos \left(\sqrt{\tfrac13}\right) \approx   \textstyle {54.7356} ^{ \circ } </math>
||arctan(sqrt(2))
|style="text-align:center;"|'''''[[Irrational number|I]]'''''
||{{OEIS2C|A195696}}
||[0;1,21,2,1,1,1,2,1,2,2,4,1,2,9,1,2,1,1,1,3,...]
||
||<small> 0.95531661812450927816385710251575775 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|0.74759 79202 53411 43517 <ref group=Mw>{{MathWorld|RenyisParkingConstant|Renyi's Parking Constant}}</ref>
||Rényi's Parking Constant <ref>{{cite book 
|author= Weisstein, Eric W
|title= Rényi's Parking Constants
|url= http://mathworld.wolfram.com/RenyisParkingConstants.html
|year=  
|publisher= MathWorld
|isbn= 
|page= (4)
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{m}</math>
||<math> \int \limits_{0}^{\infty} exp \left(\! -2 \int \limits_{0}^{x} \frac {1-e^{-y}}{y} dy\right)\! dx = {e^{-2 \gamma}} \int \limits_{0}^{\infty} \frac{e^{-2 \Gamma(0,n)}}{n^2} </math> 
||<small>[e^(-2*Gamma)] <br/>* Int{n,0,∞}[ e^(- 2<br/>*Gamma(0,n)) /n^2]</small>
||
||{{OEIS2C|A050996}}
||[0;1,2,1,25,3,1,2,1,1,12,1,2,1,1,3,1,2,1,43,...]
||
||<small> 0.74759792025341143517873094383017817 </small>  
|-

<!-------------------------------------------v------------------------------------------>
|1.44466 78610 09766 13365 <ref group=Mw>{{MathWorld|SteinersProblem|Steiner's Problem}}</ref>
||Steiner number, [[Iterated exponential]] Constant <ref>{{cite book 
|author= Eli Maor
|title= e: The Story of a Number
|url= http://books.google.com/?id=dSfaaVccJ_UC&pg=PA51&lpg=PA51&dq=1.444667861#v=onepage&q=1.444667861&f=false
|year= 2006
|publisher= Princeton University Press
|isbn= 0-691-03390-0
|page= 
}}</ref>
||<center>[[File:Infinite power tower.svg|80px]]</center>
|bgcolor=#e0f0f0 align=center|<math>\sqrt[e]{e}</math>
||<math>e^{\frac{1}{e}}{\color{White}{...........}}</math> = Upper Limit of [[Tetration]]
||e^(1/e)
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A073229}}
||[1;2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...]
||
||<small> 1.44466786100976613365833910859643022 </small> 
|-

<!-----------------------------------------v-------------------------------------------->
|0.69220 06275 55346 35386 <ref group=Mw>{{MathWorld|PowerTower|Power Tower}}</ref>
||Minimum value of función <br/> <big>ƒ</big>(x) = x<sup>x</sup> <ref>{{cite book 
|author= Clifford A. Pickover
|title= A Passion for Mathematics
|url= http://books.google.com/?id=03CVDsZSBIcC&pg=PA387&dq=Clifford+A.Pickover+%22A+passion+for+mathematics%22+0.692200#v=onepage&q=Clifford%20A.Pickover%20%22A%20passion%20for%20mathematics%22%200.692200&f=false
|year= 2005
|publisher= John Wiley & Sons, Inc.
|isbn= 0-471-69098-8
|page= 90
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math> {\left(\frac{1}{e}\right)}^\frac{1}{e}</math>
||<math>{e}^{-\frac{1}{e}} {\color{White}{..........}}</math>  = Inverse Steiner Number 
||e^(-1/e)
||
||{{OEIS2C|A072364}}
||[0;1,2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...]
||
|<small> 0.69220062755534635386542199718278976 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|0.34053 73295 50999 14282 <ref group=Mw>{{MathWorld|PolyasRandomWalkConstant|Polya's Random Walk Constant}}</ref>
||Pólya [[Random walk]] constant <ref>{{cite book 
|author= Steven R. Finch
|title= Mathematical Constants
|url= http://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA322&dq=%22P%C3%B3lya+Random+Walk%22+finch#v=onepage&q=%22P%C3%B3lya%20Random%20Walk%22%20finch&f=false
|year= 2003 
|publisher= Cambridge University Press
|isbn= 3-540-67695-3
|page= 322
}}</ref>
||[[File:Walk3d 0.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>{p(3)}</math>
||<math> 1- \!\!\left({3\over(2\pi)^3}\int\limits_{-\pi}^{\pi} \int\limits_{-\pi}^{\pi} \int\limits_{-\pi}^{\pi} {dx\,dy\,dz\over 3-\!\cos x-\!\cos y-\!\cos z}\right)^{\!-1}</math>
<math> = 1- 16\sqrt{\tfrac23}\;\pi^3 \left(\Gamma(\tfrac{1}{24})\Gamma(\tfrac{5}{24})\Gamma(\tfrac{7}{24})\Gamma(\tfrac{11}{24})\right)^{-1}</math>
||<small>1-16*Sqrt[2/3]*Pi^3 <br/>/(Gamma[1/24]<br/>*Gamma[5/24]<br/>*Gamma[7/24]<br/>*Gamma[11/24]) </small>
||
||{{OEIS2C|A086230}}
||[0;2,1,14,1,3,8,1,5,2,7,1,12,1,5,59,1,1,1,3,...]
||
||<small> 0.34053732955099914282627318443290289  </small> 
|-

<!-------------------------------------------v------------------------------------------>
|0.54325 89653 42976 70695 <ref group=Mw>{{MathWorld|LandauConstant|Landau Constant}}</ref>
||[[:de:Satz von Bloch#Landausche Konstante|Bloch–Landau constant]] <ref>{{cite book 
|author= Eric W. Weisstein
|title= CRC Concise Encyclopedia of Mathematics, Second Edition
|url= http://books.google.com/?id=aFDWuZZslUUC&pg=PA1688&dq=Bloch-Landau+constant#v=onepage&q=Bloch-Landau%20constant&f=false 
|year= 2003
|publisher= CRC Press
|isbn= 1-58488-347-2
|page= 1688
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{L}</math>
||<math> = \frac {\Gamma(\tfrac13)\;\Gamma(\tfrac{5}{6})} {\Gamma(\tfrac{1}{6})} = \frac {(-\tfrac23)!\;(-1+\tfrac56)!} {(-1+\tfrac16)!}</math>
||gamma(1/3)<br/>*gamma(5/6)<br/>/gamma(1/6)
||
||{{OEIS2C|A081760}}
||[0;1,1,5,3,1,1,2,1,1,6,3,1,8,11,2,1,1,27,4,...]
||1929
||<small> 0.54325896534297670695272829530061323 </small> 
|-

<!----------------------------------------v-------------------------------------------->
|0.18785 96424 62067 12024 <ref group=Mw>{{MathWorld|MRBConstant|MRB Constant}}</ref> <ref group=Ow>[http://oeis.org/wiki/MRB_constant MRB constant]</ref>
||[[MRB Constant]], [[Marvin Ray Burns]] <ref>{{cite book 
|author= Richard E. Crandall
|title= Unified algorithms for polylogarithm, L-series, and zeta variants
|url= http://web.archive.org/web/20130430193005/http://www.perfscipress.com/papers/UniversalTOC25.pdf
|year= 2012
|publisher= perfscipress.com
}}</ref><ref>{{cite book 
|author= RICHARD J. MATHAR
|title= NUMERICAL EVALUATION OF THE OSCILLATORY INTEGRAL OVER exp(I pi  x)x^1/x BETWEEN 1 AND INFINITY
|url= http://arxiv.org/pdf/0912.3844v3.pdf
|year= 2010 
|publisher= http://arxiv.org/abs/0912.3844
}}</ref><ref>{{cite book 
|author= M.R.Burns
|title= Root constant
|url= http://marvinrayburns.com/Original_MRB_Post.html
|year= 1999
|publisher= http://marvinrayburns.com/
}}</ref>
||[[File:MRB-Gif.gif|100px]]
|bgcolor=#e0f0f0 align=center|<math> C_{{}_{MRB}}</math>
||<math> \sum_{n=1}^{\infty} (-1)^n (n^{1/n}-1) =  - \sqrt[1]{1} + \sqrt[2]{2} - \sqrt[3]{3} + \cdots</math>
||Sum[n=1 to ∞]<br/>{(-1)^n (n^(1/n)-1)} 
||
||{{OEIS2C|A037077}}
||[0;5,3,10,1,1,4,1,1,1,1,9,1,1,12,2,17,2,2,1,...]
||1999
||<small> 0.18785964246206712024851793405427323 </small> 
|-

<!------------------------------------------v------------------------------------------->
|1.27323 95447 35162 68615
||Ramanujan–Forsyth series<ref>{{cite book 
|author= H. K. Kuiken
|title= Practical Asymptotics
|url= http://books.google.com/?id=r_-4OQ2CVY8C&pg=PA162&dq=1.2732395#v=onepage&q=1.2732395&f=false
|year= 2001 
|publisher= KLUWER ACADEMIC PUBLISHERS
|isbn= 0-7923-6920-3
|page= 162
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>\frac {4}{\pi}</math>
||<math> \displaystyle \sum \limits_{n=0}^\infty \textstyle \left(\frac{(2n-3)!!}{(2n)!!}\right)^2 = {1  \! +  \!  \left(\frac {1}{2} \right)^2  \! + \! \left(\frac {1}{2 \cdot 4} \right)^2 \! + \! \left(\frac {1 \cdot 3}{2 \cdot 4 \cdot 6} \right)^2 + \cdots}</math>
||Sum[n=0 to ∞] <br/> {[(2n-3)!! <br/> /(2n)!!]^2}
|style="text-align:center;"|'''''[[Irrational number|I]]'''''
||{{OEIS2C|A088538}}
||[1;3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,1,1,10,...]
||
||<small> 1.27323954473516268615107010698011489 </small> 
|-

<!---------------------------------------------v---------------------------------------->
|1.46707 80794 33975 47289 <ref group=Mw>{{MathWorld|PortersConstant|Porter's Constant}}</ref>
||Porter Constant<ref>{{cite book 
|author= Michel A. Théra
|title= Constructive, Experimental, and Nonlinear Analysis
|url= http://books.google.com/?id=QTcCSegK6jQC&pg=PA80&dq=%22Porter%E2%80%99s+constant%22#v=onepage&q=%22Porter%E2%80%99s%20constant%22&f=false
|year= 2002 
|publisher= CMS-AMS
|isbn= 0-8218-2167-9
|page= 77
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{C}</math>
||<math> \frac{6\ln 2}{\pi ^2} \left(3 \ln 2 + 4 \,\gamma -\frac{24}{\pi ^2} \,\zeta '(2)-2 \right)-\frac{1}{2}</math> 
<math> \scriptstyle \gamma \, \text{= Euler–Mascheroni Constant} = 0.5772156649\ldots </math>
<math> \scriptstyle \zeta '(2) \,\text{= Derivative of }\zeta(2)= 
- \sum \limits_{n = 2}^{\infty} \frac{\ln n}{n^2} = -0.9375482543\ldots </math>
||<small> 6*ln2/pi^2(3*ln2+ 4 EulerGamma- WeierstrassZeta'(2) *24/pi^2-2)-1/2 </small>
||
||{{OEIS2C|A086237}}
||[1;2,7,10,1,2,38,5,4,1,4,12,5,1,5,1,2,3,1,...]
||1974
||<small> 1.46707807943397547289779848470722995  </small> 
|-

<!---------------------------------------------v---------------------------------------->
|4.66920 16091 02990 67185 <ref group=Mw>{{MathWorld|FeigenbaumConstant|Feigenbaum Constant}}</ref>
||[[Feigenbaum constant]] δ <ref>{{cite book 
|author= Kathleen T. Alligood
|title= Chaos: An Introduction to Dynamical Systems
|url= http://books.google.com/?id=i633SeDqq-oC&pg=PA500&dq=669201609#v=onepage&q=669201609&f=false
|year= 1996  
|publisher= Springer
|isbn= 0-387-94677-2
|page= 
}}</ref>
||[[File:LogisticMap BifurcationDiagram.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>{\delta}</math>
||<math> \lim_{n \to \infty}\frac {x_{n+1}-x_n}{x_{n+2}-x_{n+1}} \qquad \scriptstyle x \in (3.8284;\, 3.8495)</math>
<math> \scriptstyle x_{n+1}=\,ax_n(1-x_n)\quad \text{or} \quad x_{n+1}=\,a\sin(x_n)</math>
||
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A006890}}
||[4;1,2,43,2,163,2,3,1,1,2,5,1,2,3,80,2,5,...]
||1975
||<small> 4.66920160910299067185320382046620161 </small> 
|-

<!------------------------------------------v------------------------------------------->
|2.50290 78750 95892 82228 <ref group=Mw>{{MathWorld|FeigenbaumConstant|Feigenbaum Constant}}</ref>
||[[Feigenbaum constant]] α<ref>{{cite book 
|author= K. T. Chau,Zheng Wang
|title= Chaos in Electric Drive Systems: Analysis, Control and Application
|url= http://books.google.com/?id=DhCbYXzLFLsC&pg=PA7&dq=2.502907875095892822283902873218#v=onepage&q=2.502907875095892822283902873218&f=false
|year= 201  
|publisher= John Wiley & Son
|isbn= 978-0-470-82633-1
|page= 7 
}}</ref>
||[[File:Mandelbrot zoom.gif|100px]]
|bgcolor=#e0f0f0 align=center|<math>\alpha</math>
||<math>\lim_{n \to \infty}\frac {d_n}{d_{n+1}}</math>
||
|style="text-align:center;"|'''''[[Transcendental number|T]]''''' ?
||{{OEIS2C|A006891}}
||[2;1,1,85,2,8,1,10,16,3,8,9,2,1,40,1,2,3,...]
||1979
||<small> 2.50290787509589282228390287321821578 </small> 
|-

<!----------------------------------------------v--------------------------------------->
|0.62432 99885 43550 87099 <ref group=Mw>{{MathWorld|Golomb-DickmanConstant|Golomb-Dickman Constant}}</ref>
||[[Golomb–Dickman constant]] <ref>{{cite book 
|author= Eric W. Weisstein
|title= CRC Concise Encyclopedia of Mathematics
|url= http://books.google.com/?id=aFDWuZZslUUC&pg=PA1211&lpg=PA1211&dq=Golomb%E2%80%93Dickman+constant#v=onepage&q=Golomb%E2%80%93Dickman%20constant&f=false
|year= 2002
|publisher= Crc Press
|isbn= 
|page= 1212
}}</ref>
||<br><br><br>
|bgcolor=#e0f0f0 align=center|<math>{\lambda}</math>
||<math>\int \limits_0^\infty \underset{\text{Para } x>2}{\frac{f(x)}{x^2} \, dx} = \int \limits_0^1 e^{\operatorname{Li}(n)} dn \quad \scriptstyle \text{Li: Logarithmic integral}</math>
||N[Int{n,0,1}[e^Li(n)],34]
||
||{{OEIS2C|A084945}}
||[0;1,1,1,1,1,22,1,2,3,1,1,11,1,1,2,22,2,6,1,...]
||1930 <br> & <br> 1964
||<small> 0.62432998854355087099293638310083724 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|23.14069 26327 79269 0057 <ref group=Mw>{{MathWorld|GelfondsConstant|Gelfonds Constant}}</ref>
||[[Gelfond constant]] <ref>{{cite book 
|author= David Wells
|title= The Penguin Dictionary of Curious and Interesting Numbers
|url= http://books.google.com/?id=7L7xcjBPemEC&pg=RA2-PA4&dq=23.14069#v=onepage&q=23.14069&f=false
|year= 1997
|publisher= Penguin Books Ltd.
|isbn= 
|page= 4
}}</ref>
||<br><br><br>
|bgcolor=#e0f0f0 align=center|<math>{e}^{\pi}</math>
||<math> (-1)^{-i} = i^{-2i} = \sum_{n=0}^\infty \frac{\pi^{n}}{n!} = \frac{\pi^{1}}{1} + \frac{\pi^{2}}{2!} + \frac{\pi^{3}}{3!} + \cdots</math>
||Sum[n=0 to ∞] <br/> {(pi^n)/n!}
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A039661}}
||[23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,...]
||
||<small> 23.1406926327792690057290863679485474 </small>
<!-- 0.04321391826377224977441773717172801<br> ''1/C = (-1)^i = e^-pi'' = {{OEIS2C|A093580}} -->
|-

<!---------------------------------------------v---------------------------------------->
|7.38905 60989 30650 22723
||[[Conic constant]], [[Schwarzschild constant]] <ref>{{cite book 
|author= Jvrg Arndt,Christoph Haenel
|title= Pi: Algorithmen, Computer, Arithmetik
|url= http://books.google.com/?id=mchJCvIsSXwC&pg=PA67&dq=7.38905#v=onepage&q=7.38905&f=false
v|year=  
|publisher= Springer
|isbn= 3-540-66258-8
|page= 67
}}</ref>
||[[File:Conic constant.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>e^2</math>
||<math> \sum_{n = 0}^\infty \frac{2^n}{n!} = 1+2+\frac{2^2}{2!}+\frac{2^3}{3!}+\frac{2^4}{4!}+\frac{2^5}{5!}+\cdots</math>
|| Sum[n=0 to ∞]<br/>{2^n/n!}
||
||{{OEIS2C|A072334}}
||[7;2,1,1,3,18,5,1,1,6,30,8,1,1,9,42,11,1,...]<br>= [7,2,{{overline|1,1,n,4*n+6,n+2}}], n = 3, 6, 9, etc.
||
||<small> 7.38905609893065022723042746057500781 </small> 
|-

<!------------------------------------------v------------------------------------------->
|0.35323 63718 54995 98454 <ref group=Mw>{{MathWorld|Hafner-Sarnak-McCurleyConstant|Hafner-Sarnak-McCurley Constant}}</ref>
||[[Hafner–Sarnak–McCurley constant]] (1) <ref>{{cite book 
|author= Steven R. Finch
|title= Mathematical Constants
|url= http://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA110&dq=%22Hafner-Sarnak-McCurley+constant%22#v=onepage&q=%22Hafner-Sarnak-McCurley%20constant%22&f=false
|year= 2003
|publisher= 
|isbn= 3-540-67695-3
|page= 110
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{\sigma}</math>
||<math> \prod_{k=1}^{\infty}\left\{1-[1-\prod_{j=1}^n \underset{p_k: \text{ prime}}{(1-p_k^{-j})]^2}\right\}</math>
||prod[k=1 to ∞] {1-(1-prod[j=1 to n] {1-ithprime(k)^-j})^2} 
||
||{{OEIS2C|A085849}}
||[0;2,1,4,1,10,1,8,1,4,1,2,1,2,1,2,6,1,1,1,3,...]
||1993
||<small> 0.35323637185499598454351655043268201  </small> 
|-

<!------------------------------------------v------------------------------------------->
|0.60792 71018 54026 62866 <ref group=Mw>{{MathWorld|RelativelyPrime|Relatively Prime}}</ref>
||[[Hafner–Sarnak–McCurley constant]] (2) <ref>{{cite book 
|author= Holger Hermanns,Roberto Segala
|title= Process Algebra and Probabilistic Methods.
|url= http://books.google.com/?id=007-3SM9QmYC&pg=PA270&dq=0.607927101854026628663276779#v=onepage&q=0.607927101854026628663276779&f=false
|year= 2000
|publisher= Springer-Verlag
|isbn= 3-540-67695-3
|page= 270
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>\frac{1}{\zeta(2)}</math>
||<math> \frac{6}{\pi^2} = \prod_{n = 0}^\infty \underset{p_n: \text{ prime}}{\! \left(\! 1- \frac{1}{{p_n}^2} \! \right)} \! = \! \textstyle \left(1 \! - \! \frac{1}{2^2}\right) \! \left(1 \! - \! \frac{1}{3^2}\right) \! \left(1 \! - \! \frac{1}{5^2}\right)\cdots</math>
||Prod{n=1 to ∞}<br/>(1-1/ithprime(n)^2) 
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A059956}}
||[0;1,1,1,1,4,2,4,7,1,4,2,3,4,10,1,2,1,1,1,...] 
||
||<small> 0.60792710185402662866327677925836583 </small> 
|-

<!------------------------------------------v------------------------------------------->
|0.12345 67891 01112 13141 <ref group=Mw>{{MathWorld|ChampernowneConstant|Champernowne Constant}}</ref>
||[[Champernowne constant]] <ref>{{cite book 
|author= Michael J. Dinneen,Bakhadyr Khoussainov,Prof. Andre Nies
|title= Computation, Physics and Beyond
|url= http://books.google.com/?id=wRWyMbmJTMYC&pg=PA109&dq=%22Champernowne+number%22#v=onepage&q=%22Champernowne%20number%22&f=false
|year= 2012 
|publisher= Springer
|isbn= 978-3-642-27653-8
|page= 110 
}}</ref>
||[[File:Champernowne constant.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>C_{10}</math>
||<math>\sum_{n=1}^\infty \; \sum_{k=10^{n-1}}^{10^n-1}\frac{k}{10^{kn-9\sum_{j=0}^{n-1}10^j(n-j-1)}}</math>
||
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A033307}}
||[0;8,9,1,149083,1,1,1,4,1,1,1,3,4,1,1,1,15,...]
||1933
||<small> 0.12345678910111213141516171819202123 </small>  
|-

<!-----------------------------------------v-------------------------------------------->
|0.76422 36535 89220 66299 <ref group=Mw>{{MathWorld|Landau-RamanujanConstant|Landau-Ramanujan Constant}}</ref>
||[[Landau-Ramanujan constant]] <ref>{{cite book 
|author= Richard E. Crandall,Carl B. Pomerance
|title= Prime Numbers: A Computational Perspective
|url=http://books.google.com/?id=ZXjHKPS1LEAC&pg=PA80&dq=Landau-Ramanujan+constant#v=onepage&q=Landau-Ramanujan%20constant&f=false 
|year= 2005  
|publisher= Springer
|isbn= 978-0387-25282-7
|page= 80
}}</ref>
||<br><br><br><br>
|bgcolor=#e0f0f0 align=center|<math>K</math>
||<math>\frac1{\sqrt2}\prod_{p\equiv3\!\!\!\!\!\mod \! 4}\!\! \underset{\!\!\!\!\!\!\!\! p: \text{ prime}}{\left(1-\frac1{p^2}\right)^{-\frac{1}{2}}}\!\!=\frac\pi4\prod_{p\equiv1\!\!\!\!\!\mod \!4}\!\! \underset{\!\!\!\! p: \text{ prime}}{\left(1-\frac1{p^2}\right)^\frac{1}{2}}</math>
||
|style="text-align:center;"|'''''[[Transcendental number|T]]''''' ?
||{{OEIS2C|A064533}}
||[0;1,3,4,6,1,15,1,2,2,3,1,23,3,1,1,3,1,1,6,4,...]
||
||<small> 0.76422365358922066299069873125009232 </small>  
|-

<!---------------------------------------------v---------------------------------------->
|1.92878 00... <ref group=Mw>{{MathWorld|PrimeFormulas|PrimeFormulas}}</ref>
||Wright constant <ref>{{cite book 
|author= Paulo Ribenboim 
|title= My Numbers, My Friends: Popular Lectures on Number Theory
|url= http://books.google.com/?id=EiYvlcimEi4C&pg=PA66&dq=1.9287800#v=onepage&q=1.9287800&f=false
|year= 2000 
|publisher= Springer-Verlag
|isbn= 0-387-98911-0
|page= 66 
}}</ref>
||<br><br><br>
|bgcolor=#e0f0f0 align=center|<math>{\omega}</math>
||<math>\left \lfloor 2^{2^{2^{\cdot^{\cdot^{2^{\omega}}}}}} \!\right \rfloor \scriptstyle \text{= primes:} \displaystyle\left\lfloor 2^\omega\right\rfloor \scriptstyle \text{=3,} 
\displaystyle\left\lfloor 2^{2^\omega} \right\rfloor \scriptstyle \text{=13,} 
\displaystyle \left\lfloor 2^{2^{2^\omega}} \right\rfloor \scriptstyle =16381, \ldots </math>
||
||
||{{OEIS2C|A086238}}
||[1; 1, 13, 24, 2, 1, 1, 3, 1, 1, 3]
||
||1.9287800...
|-

<!------------------------------------------v------------------------------------------->
|2.71828 18284 59045 23536 <ref group=Mw>{{MathWorld|e|e}}</ref>
||[[Number e]], Euler's number <ref>{{cite book
|author= E.Kasner y J.Newman.
|title= Mathematics and the Imagination
|pages= 77
|year= 2007
|publisher= Conaculta
|isbn= 978-968-5374-20-0
|url= http://books.google.com/?id=zdBHMHV3m5YC&pg=PA76&dq=2.7182818284590452353602874#v=onepage&q=2.7182818284590452353602874&f=false
}}</ref>
||[[File:Exp derivative at 0.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{e}</math>
||<math>\! \lim_{n \to \infty} \! \left( \! 1 \! + \! \frac {1}{n}\right)^n \! = \! \sum_{n = 0}^\infty \frac{1}{n!} = \frac{1}{0!} + \frac{1}{1} + \frac{1}{2!} + \frac{1}{3!} + \textstyle \cdots </math>
||Sum[n=0 to ∞]<br/>{1/n!}    <!--- lim_(n->∞) (1+1/n)^n --->
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A001113}}
||[2;1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...] <br> = [2;{{overline|1,2p,1}}],  p∈ℕ
||
||<small> 2.71828182845904523536028747135266250 </small> 
|-

<!--------------------------------------------v----------------------------------------->
|0.36787 94411 71442 32159 <ref group=Mw>{{MathWorld|FactorialSums|Factorial Sums}}</ref>
||Inverse of [[Number e]] <ref>{{cite book 
|author= Eli Maor 
|title= "e": The Story of a Number
|url= http://books.google.com/?id=eIsyLD_bDKkC&pg=PA37&dq=0.367879441#v=onepage&q=0.367879441&f=false
|year= 1994 
|publisher= Princeton University Press
|isbn= 978-0-691-14134-3
|page= 37
}}</ref>
||<br><br><br>
|bgcolor=#e0f0f0 align=center|<math>\frac{1}{e}</math>
||<math>\sum_{n = 0}^\infty \frac{(-1)^n}{n!} = \frac{1}{0!} - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \frac{1}{5!} +\cdots</math>
<!--- 2\cdot(1/3! +2/5! +3/7!+\cdots --->
||Sum[n=2 to ∞]<br/>{(-1)^n/n!}
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A068985}}
||[0;2,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,...] <br> = [0;2,1,{{overline|1,2p,1}}],  p∈ℕ
||1618
||<small> 0.36787944117144232159552377016146086 </small> 
|-

<!----------------------------------------------v--------------------------------------->
|0.69034 71261 14964 31946
||Upper [[iterated exponential]] <ref>{{cite book 
|author= Theo Kempermann
|title= Zahlentheoretische Kostproben
|url= http://books.google.com/?id=c70frvZ9TEQC&pg=PA139&lpg=PA139&dq=0.690347+0.658366#v=onepage&q=0%2C690347%200%2C658366&f=false
|year= 2005
|publisher= Freiburger graphische betriebe
|isbn= 3-8171-1780-9
|page= 139
}}</ref>
||[[Image:TetrationConvergence2D.png|100px]]
|bgcolor=#e0f0f0 align=center|<math> {H}_{2n+1} </math>
||<math> \lim_{n \to \infty} {H}_{2n+1} = 
\textstyle \left(\frac{1}{2}\right)
^{\left(\frac{1}{3}\right)
^{\left(\frac{1}{4}\right)
^{\cdot^{\cdot^{\left(\frac{1}{2n+1}\right)}}}}}
 = {2}^{-3^{-4^{\cdot^{\cdot^{{-2n-1}}}}}} </math> 
||2^-3^-4^-5^-6^ <br/> -7^-8^-9^-10^ <br/> -11^-12^-13 …
||
||{{OEIS2C|A242760}}
||[0;1,2,4,2,1,3,1,2,2,1,4,1,2,4,3,1,1,10,1,3,2,...]
||
||<small> 0.69034712611496431946732843846418942 </small>
|-

<!--------------------------------------------v----------------------------------------->
|0.65836 55992 ...  
||Lower límit [[iterated exponential]] <ref>{{cite book 
|author= Steven Finch
|title= Mathematical Constants
|url=http://books.google.com/?id=DL5iVYNoEa0C&pg=PA449&lpg=PA449&dq=0.6583655992#v=onepage&q=0.6583655992&f=false
|year= 2003 
|publisher= Cambridge University Press 
|isbn= 0-521-81805-2
|page= 449
}}</ref>
||
 |bgcolor=#e0f0f0 align=center|<math> {H}_{2n} </math>
||<math> \lim_{n \to \infty} {H}_{2n} = 
\textstyle \left(\frac{1}{2}\right)
^{\left(\frac{1}{3}\right)
^{\left(\frac{1}{4}\right)
^{\cdot^{\cdot^{\left(\frac{1}{2n}\right)}}}}}
 = {2}^{-3^{-4^{\cdot^{\cdot^{{-2n}}}}}} </math> 
||2^-3^-4^-5^-6^ <br/> -7^-8^-9^-10^ <br/> -11^-12 …
||
||
||[0;1,1,1,12,1,2,1,1,4,3,1,1,2,1,2,1,51,2,2,1,...]
||
||0.6583655992...  
|-

<!------------------------------------------v------------------------------------------->
|3.14159 26535 89793 23846 <ref group=Mw>{{MathWorld|PiFormulas|Pi Formulas}}</ref>
||[[pi|π number]], [[Archimedes number]] <ref>{{cite book 
|author= Michael Trott
|title= The Mathematica GuideBook for Programming
|url=  http://books.google.com/?id=iZTxaxT_YeMC&pg=PA173&dq=pi+nested+radical#v=onepage&q=pi%20nested%20radical&f=false 
|year= 2004
|publisher= Springer Science
|isbn= 0-387-94282-3
|page= 173
}}</ref>
||[[File:Sine cosine one period.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math> \pi </math>
||<math>\lim_{n\to \infty }\, 2^n \underbrace{\sqrt{2-\sqrt{2+\sqrt{2+\cdots +\sqrt{2}}}}}_n</math>
||Sum[n=0 to ∞]<br/>{(-1)^n 4/(2n+1)}  
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A000796}}
||[3;7,15,1,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,...]
||
||<small> 3.14159265358979323846264338327950288 </small> 
|-

<!-----------------------------------------v-------------------------------------------->
|0.46364 76090 00806 11621
||Machin–Gregory series<ref>{{cite book 
|author= John Horton Conway, Richard K. Guy.
|title= The Book of Numbers
|url= http://books.google.com/?id=0--3rcO7dMYC&pg=PA242&dq=%22The+Book+of+Numbers%22+%22mathematician+David+Gregory%22#v=onepage&q=%22The%20Book%20of%20Numbers%22%20%22mathematician%20David%20Gregory%22&f=false
|year= 1995
|publisher= Copernicus
|isbn= 0-387-97993-X
|page= 242
|quote=
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>\arctan \frac {1}{2}</math>
||<math>  \underset{\text{For } x = 1/2 \qquad \qquad} {\sum_{n=0}^\infty \frac{(\!-1\!)^n \, x^{2n+1}}{2n+1} = \frac {1}{2} {-} \frac{1}{3 \! \cdot \! 2^3} {+} \frac{1}{5 \! \cdot \! 2^5} {-} \frac{1}{7 \! \cdot \! 2^7} {+} \cdots}</math>
||Sum[n=0 to ∞] <br/> {(-1)^n (1/2)^(2n+1)<br/>/(2n+1)}
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||{{OEIS2C|A073000}}
||[0;2,6,2,1,1,1,6,1,2,1,1,2,10,1,2,1,2,1,1,1,...]
||
||<small> 0.46364760900080611621425623146121440  </small> 
|-

<!--------------------------------------------v----------------------------------------->
|1.90216 05831 04 <ref group=Mw>{{MathWorld|BrunsConstant|Brun's Constant}}</ref>
||<small>[[Brun's constant|Brun<sub> 2 </sub> constant]] = Σ inverse of [[Twin prime]]s</small> <ref>{{cite book 
|author= Thomas Koshy
|title= Elementary Number Theory with Applications
|url= http://books.google.com/?id=d5Z5I3gnFh0C&pg=PA118&dq=Brun+constant#v=onepage&q=Brun%20constant&f=false
|year= 2007
|publisher= Elsevier
|isbn= 978-0-12-372-487-8
|page= 119
}}</ref>
||[[File:Bruns-constant.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{B}_{\,2}</math>
||<math> \textstyle \underset{ p,\, p+2: \text{ prime}}{\sum(\frac1{p}+\frac1{p+2})} = (\frac1{3} \! + \! \frac1{5}) + (\tfrac1{5} \! + \! \tfrac1{7}) + (\tfrac1{11} \! + \! \tfrac1{13}) + \cdots </math>
||
||
||{{OEIS2C|A065421}}
||[1; 1, 9, 4, 1, 1, 8, 3, 4, 4, 2, 2]
||
||1.902160583104 
|-

<!-------------------------------------------v------------------------------------------>
|0.87058 83799 75 <ref group=Mw>{{MathWorld|BrunsConstant|Brun's Constant}}</ref>
||<small>[[Brun's constant|Brun<sub> 4 </sub> constant]] = Σ inv.[[prime quadruplet]]s</small> <ref>{{cite book 
|author= Pascal Sebah and Xavier Gourdon
|title= Introduction to twin primes and Brun’s constant computation
|url= http://numbers.computation.free.fr/Constants/Primes/twin.pdf
|year= 2002
|publisher= 
|isbn= 
|page= 
}}</ref>
||<br><br><br><br>
|bgcolor=#e0f0f0 align=center|<math>{B}_{\,4}</math>
||<math>\textstyle {\sum(\frac1{p}+\frac1{p+2}+\frac1{p+4}+\frac1{p+6})} \scriptstyle \quad {p,\; p+2,\; p+4,\; p+6: \text{ prime}} </math>
<math> \textstyle{\left(\tfrac1{5} + \tfrac1{7} + \tfrac1{11} + \tfrac1{13}\right)}+ \left(\tfrac1{11} + \tfrac1{13} + \tfrac1{17} + \tfrac1{19}\right)+ \dots</math>
||
||
||{{OEIS2C|A213007}}
||[0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1]
||
||0.870588379975 
|-

<!------------------------------------------v------------------------------------------->
|0.63661 97723 67581 34307 <ref group=Mw>{{MathWorld|PrimeProducts|Prime Products}}</ref>
<ref group=Ow>[http://oeis.org/wiki/Buffon%27s_constant Buffon's constant]</ref>
||Buffon constant<ref>{{cite book
|author= Jorg Arndt,Christoph Haenel
|title= Pi -- Unleashed
|page= 13
|year= 2000
|publisher= Verlag Berlin Heidelberg
|isbn= 3-540-66572-2
|url= http://books.google.com/?id=QwwcmweJCDQC&pg=PA13&dq=Fran%C3%A7ois+Vi%C3%A8te+(1540-1603)+developed#v=onepage&q=Fran%C3%A7ois%20Vi%C3%A8te%20(1540-1603)%20developed&f=false
}}</ref>
||[[Image:Viète nested polygons.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>\frac{2}{\pi}</math>
||<math> \frac{\sqrt2}2 \cdot \frac{\sqrt{2+\sqrt2}}2 \cdot \frac{\sqrt{2+\sqrt{2+\sqrt2}}}2 \cdots</math>
[[Viète's formula|Viète product]]
||2/Pi
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A060294}}
||[0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...]
||1540 <br> to <br> 1603
||<small> 0.63661977236758134307553505349005745 </small> 
|-

<!--------------------------------------------v----------------------------------------->
|0.59634 73623 23194 07434 <ref group=Mw>{{MathWorld|GompertzConstant|Gompertz Constant}}</ref>
||[[Gompertz constant|Euler–Gompertz constant]] <ref>{{cite book 
|author= Annie Cuyt, Viadis Brevik Petersen, Brigitte Verdonk, William B. Jones
|title= Handbook of continued fractions for special functions
|url= http://books.google.com/?id=DQtpJaEs4NIC&pg=PA190&dq=Gompertz+constant#v=onepage&q=Gompertz%20constant&f=false
|year= 2008
|publisher= Springer Science 
|isbn= 978-1-4020-6948-2
|page= 190
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{G}</math>
||<math>\! \int \limits_0^\infty \!\! \frac{e^{-n}}{1{+}n} \, dn = \!\! \int \limits_0^1 \!\! \frac{1}{1{-}\ln n} \, dn =
 \textstyle {\tfrac 1 {1+\tfrac 1{1+\tfrac 1{1+\tfrac 2{1+\tfrac 2{1+\tfrac 3{1+3{/\cdots}} }}}}}} </math>
<!--- 1/(1+1/(1+1/(1+2/(1+2/(1+3/(1+3))))))) demo Wolfram --->
||integral[0 to ∞]<br/>{(e^-n)/(1+n)}
||
||{{OEIS2C|A073003}}
||[0;1,1,2,10,1,1,4,2,2,13,2,4,1,32,4,8,1,1,1,...]
<!--- 1/(1+1/(1+1/(2+1/(10+1/(1+1/(1+1/(4+1))))))) demo Wolfram --->
||
||<small> 0.59634736232319407434107849936927937 </small> 
|-

<!----------------------------------------v--------------------------------------------->
|<center> '''''i'''''  ··· <ref group=Mw>{{MathWorld|i|i}}</ref> </center>
||[[Imaginary number]] <ref>{{cite book 
|author= Keith J. Devlin 
|title= Mathematics: The New Golden Age
|url= http://books.google.com/?id=IKmMKOtSI50C&pg=PA66&dq=%22This+leads+to+some+amazing+results.+For+example,+Euler+discovered%22#v=onepage&q=%22This%20leads%20to%20some%20amazing%20results.%20For%20example%2C%20Euler%20discovered%22&f=false
|year= 1999
|publisher= Columbia University Press
|isbn= 0-231-11638-1
|page= 66
}}</ref>
||[[Image:Complex numbers imaginary unit.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{i}</math>
||<math>\sqrt{-1} = \frac{\ln(-1)}{\pi} \qquad\qquad \mathrm{e}^{i\,\pi} = -1</math>
||sqrt(-1)
|style="text-align:center;"|'''''[[Complex number|C]]'''''
|| 
||
||1501 <br/> to <br/> 1576
||<center> '''''i''''' </center>
|-

<!--------------------------------------------v----------------------------------------->
|0.69777 46579 64007 98200 <ref group=Mw>{{MathWorld|ContinuedFractionConstant|ContinuedFraction Constant}}</ref>
||Continued fraction constant, [[Bessel function]]<ref>{{cite book
|author= Simon Plouffe
|title= Miscellaneous Mathematical Constants
|url= http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap69.html
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{C}_{CF}</math>
||<math> \frac{I_1(2)}{I_0(2)} = \frac{ \sum \limits_{n = 0}^\infty \frac{n}{n!n!}} {{ \sum \limits_{n = 0}^{\infty} \frac{1}{n!n!}}} =
 \textstyle \tfrac 1{1+\tfrac 1{2+\tfrac 1{3+\tfrac 1{4+\tfrac 1{5+\tfrac 1{6+1{/\cdots}}}}}}} </math>
<!--- 1/(1+1/(1+1/(1+2/(1+2/(1+3/(1+3/(1+4))))))) demo Wolfram --->
||(Sum [n=0 to ∞]<br/>{n/(n!n!)}) /<br/>(Sum [n=0 to ∞]<br/>{1/(n!n!)})
||
||{{OEIS2C|A052119}}
||[0;1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,...] <br> = [0;{{overline|p+1}}],  p∈ℕ
<!--- 1/(1+1/(2+1/(3+1/(4+1/(5+1/(6+1/(7+1/(8+1))))))))--->
||
||<small> 0.69777465796400798200679059255175260 </small> 
|-

<!---------------------------------------------v---------------------------------------->
|2.74723 82749 32304 33305
||[[Ramanujan]] [[nested radical]] <ref>{{cite book 
|author= Bruce C. Berndt,Robert Alexander Rankin
|title= Ramanujan: essays and surveys
|url= http://books.google.com/?id=TT1T8A94xNcC&pg=PA219&dq=Ramanujan+nested+radical#v=onepage&q=Ramanujan%20nested%20radical&f=false
|year= 2001 
|publisher= American Mathematical Society, London Mathematical Society
|isbn= 0-8218-2624-7
|page= 219
}}</ref>
||<br><br><br><br>
|bgcolor=#e0f0f0 align=center|<math> R_{5} </math>
||<math>\scriptstyle \sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+
                     \sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}}\;=
        \textstyle\frac{2+\sqrt{5}+\sqrt{15-6\sqrt{5}}}{2}</math>
||(2+sqrt(5)<br/>+sqrt(15<br/>-6 sqrt(5)))/2
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||
||[2;1,2,1,21,1,7,2,1,1,2,1,2,1,17,4,4,1,1,4,2,...]
||
||<small> 2.74723827493230433305746518613420282 </small> 
|-

<!------------------------------------------v------------------------------------------->
|0.56714 32904 09783 87299 <ref group=Mw>{{MathWorld|OmegaConstant|Omega Constant}}</ref>
||[[Omega constant]], [[Lambert W function]] <ref>{{cite book 
|author= Albert Gural 
|title= Infinite Power Towers
|url= http://www.albertgural.com/math/theory/infinite-power-towers/
}}</ref>
||[[File:Lambert-w.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{\Omega}</math>
||<math> \sum_{n=1}^\infty \frac{(-n)^{n-1}}{n!} 
 =\,\left(\frac{1}{e}\right)
^{\left(\frac{1}{e}\right)
^{\cdot^{\cdot^{\left(\frac{1}{e}\right)}}}}
= e^{-\Omega} = e^{-e^{-e^{\cdot^{\cdot^{{-e}}}}}} </math> 
||Sum[n=1 to ∞]<br/>{(-n)^(n-1)/n!}
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A030178}}
||[0;1,1,3,4,2,10,4,1,1,1,1,2,7,306,1,5,1,2,1,...]
||
||<small> 0.56714329040978387299996866221035555 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|0.96894 61462 59369 38048
||[[Dirichlet beta function|Beta]](3) <ref>{{cite book 
|author= Michael A. Idowu
|title= Fundamental relations between the Dirichlet beta function, euler numbers, and Riemann zeta function for positive integers
|url= http://arxiv.org/abs/1210.5559
|year= 2012
|publisher= arXiv:1210.5559  
|isbn= 
|page= 1
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{\beta} (3)</math>
|| <math> \frac{\pi^3}{32} = \sum_{n=1}^\infty\frac{-1^{n+1}}{(-1+2n)^3} = \frac{1}{1^3} {-} \frac{1}{3^3} {+} \frac{1}{5^3} {-} \frac{1}{7^3} {+} \cdots </math>
||Sum[n=1 to ∞]<br/>{(-1)^(n+1)<br/>/(-1+2n)^3}
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A153071}}
||[0;1,31,4,1,18,21,1,1,2,1,2,1,3,6,3,28,1,...]
||
||<small> 0.96894614625936938048363484584691860 </small> 
|-

<!------------------------------------------v------------------------------------------->
|2.23606 79774 99789 69640
||[[Square root of 5]], [[Gauss sum]] <ref>{{cite book 
|author= P A J Lewis  
|title= Essential Mathematics 9
|url= http://books.google.com/?id=KjMVx6ljh6YC&pg=PA24&dq=2.236067977#v=onepage&q=2.236067977&f=false
|year= 2008
|publisher= Ratna Sagar
|isbn= 9788183323673
|page= 24
|quote=
}}</ref>
||[[File:Pinwheel 1.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math> \sqrt{5} </math>
||<math> \scriptstyle  (n = 5) \displaystyle  \sum_{k=0}^{n-1} e^{\frac{2 k^2 \pi i}{n}} = 1 + e^\frac{2 \pi i} {5} + e^\frac{8 \pi i} {5} + e^\frac{18 \pi i} {5} + e^\frac{32 \pi i} {5}</math>
||Sum[k=0 to 4]<br/>{e^(2k^2 pi i/5)}
|style="text-align:center;"|'''''[[Algebraic number|A]]'''''
||{{OEIS2C|A002163}}
||[2;4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,...] <br> = [2;{{overline|4}},...]
||
||<small> 2.23606797749978969640917366873127624 </small> 
|-

<!--------------------------------------------v----------------------------------------->
|3.35988 56662 43177 55317 <ref group=Mw>{{MathWorld|ReciprocalFibonacciConstant|Reciprocal Fibonacci Constant}}</ref>
||Prévost constant [[Reciprocal Fibonacci constant]]<ref>{{cite book 
|author= Gérard P. Michon
|title= Numerical Constants
|url= http://www.numericana.com/answer/constants.htm#prevost
|year= 2005
|publisher= Numericana
|isbn= 
|page= 
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math> \Psi </math>
||<math>\sum_{n=1}^{\infty} \frac{1}{F_n} = \frac{1}{1} +  \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{8} + \frac{1}{13} + \cdots</math>
F<sub>n</sub>: [[Fibonacci series]]
||Sum[n=1 to ∞]<br/>{1/Fibonacci[n]}
|style="text-align:center;"|'''''[[Irrational number|I]]'''''
||{{OEIS2C|A079586}}
||[3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...]
||?
||<small> 3.35988566624317755317201130291892717 </small> 
|-

<!------------------------------------------v------------------------------------------->
|{{nobr|2.68545 20010 65306 44530}}&nbsp;<ref group=Mw>{{MathWorld|KhinchinsConstant|Khinchin's Constant}}</ref>
||[[Khinchin's constant]] <ref>{{cite book 
|author= Julian Havil
|title= Gamma: Exploring Euler's Constant
|url=http://books.google.com/?id=7-sDtIy8MNIC&pg=PA161&dq=Khinchin%27s+constant#v=onepage&q=Khinchin%27s%20constant&f=false
|year= 2003 
|publisher= Princeton University Press
|isbn= 9780691141336 
|page= 161
}}</ref>
||[[File:KhinchinBeispiele.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math> K_{\,0} </math>
||<math> \prod_{n=1}^\infty \left[{1+{1\over n(n+2)}}\right]^{\ln n/\ln 2}</math>
||Prod[n=1 to ∞] <br/> {(1+1/(n(n+2))) <br/> ^(ln(n)/ln(2))}
|style="text-align:center;"|'''''[[Transcendental number|T]]'''''
||{{OEIS2C|A002210}}
||[2;1,2,5,1,1,2,1,1,3,10,2,1,3,2,24,1,3,2,...]
||1934
||<small> 2.68545200106530644530971483548179569 </small> 
|-

<!-------------------------------------------.------------------------------------------>
|}


==References==
{{reflist}}