View source for Wikipedia:WikiProject Mathematics/PlanetMath Exchange/33-XX Special functions

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{{Planetmath instructions|topic=33-XX Special functions}}

==33-00 General reference works (handbooks, dictionaries, bibliographies, etc.)==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6269 index of special functions], id=6269 -- WP: [[list of mathematical functions]] -- Status: '''A'''
::[[User:Linas|linas]] 21:49, 13 Mar 2005 (UTC)

==33B10 Exponential and trigonometric functions==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=2666 natural logarithm], id=2666 -- WP: [[natural logarithm]] -- Status: '''A'''
::[[User:Linas|linas]] 15:54, 13 Mar 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7395 Exact Trigonometry Tables], id=7395 -- WP: [[Exact Trigonometry Tables]] -- Status:'''N'''
::Curious. [[User:Linas|linas]] 20:41, 5 March 2006 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=9798 proof of angle sum identities], id=9798<sup><span style="color:red;">new!</span></sup> -- WP guess: [[proof of angle sum identities]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6807 trigonometry], id=6807<sup><span style="color:red;">new!</span></sup> -- WP guess: [[trigonometry]] -- Status:

==33B15 Gamma, beta and polygamma functions==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=3730 Bohr-Mollerup theorem], id=3730 -- WP: [[Bohr-Mollerup theorem]] -- Status: '''A'''
::[[User:Linas|linas]] 21:54, 13 Mar 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6206 evaluation of beta function using Laplace transform], id=6206 -- WP: [[Beta function]] -- Status: '''NM'''
::<s>This article provides a derivation/proof of a result quoted in main WP math articles.  As such, I believe it could be useful to copy this article, as it helps establish the correctness and consistency of WP math articles. However, one may also argue that such proofs are un-needed as long as the accuracy of WP articles remains unchallenged. [[User:Linas|linas]] 16:35, 26 Mar 2005 (UTC)</s>
::Its short, just merge it into [[beta function]]. [[User:Linas|linas]] 20:37, 5 March 2006 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6576 proof of Bohr-Mollerup theorem], id=6576 -- WP: [[Bohr-Mollerup theorem]] -- Status: '''N'''
::This article provides a derivation/proof of a result quoted in main WP math articles.  As such, I believe it could be useful to copy this article, as it helps establish the correctness and consistency of WP math articles. However, one may also argue that such proofs are un-needed as long as the accuracy of WP articles remains unchallenged. [[User:Linas|linas]] 16:35, 26 Mar 2005 (UTC)
::Change to '''N'''. [[User:Linas|linas]] 20:30, 5 March 2006 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=3808 proof of Bohr-Mollerup theorem], id=3808 -- WP: [[Bohr-Mollerup theorem]] -- Status: '''N'''
::This article provides a derivation/proof of a result quoted in main WP math articles.  As such, I believe it could be useful to copy this article, as it helps establish the correctness and consistency of WP math articles. However, one may also argue that such proofs are un-needed as long as the accuracy of WP articles remains unchallenged. [[User:Linas|linas]] 16:35, 26 Mar 2005 (UTC)
::Change to '''N'''. [[User:Linas|linas]] 20:32, 5 March 2006 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4001 beta function], id=4001 -- WP: [[beta function]] -- Status: '''A'''
::[[User:Linas|linas]] 20:25, 5 March 2006 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=9481 alternate integral representation of beta function], id=9481<sup><span style="color:red;">new!</span></sup> -- WP guess: [[alternate integral representation of beta function]] -- Status:

==33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6429 error function], id=6429 -- WP: [[error function]] -- Status: '''A'''
::[[User:Linas|linas]] 16:04, 13 Mar 2005 (UTC)

==33B30 Higher logarithm functions==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=2957 Lambert W function], id=2957 -- WP: [[Lambert W function]] -- Status: '''A'''
::[[User:Linas|linas]] 22:05, 13 Mar 2005 (UTC)

==33B99 Miscellaneous==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=657 natural log base], id=657 -- WP: [[Base of the natural logarithm]] -- Status: '''A'''
::[[User:Linas|linas]] 22:03, 13 Mar 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7775 (1 + 1/n)^n is an increasing sequence], id=7775<sup><span style="color:red;">new!</span></sup> -- WP guess: [[(1 + 1/n)^n is an increasing sequence]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7778 bounds for e], id=7778<sup><span style="color:red;">new!</span></sup> -- WP guess: [[bounds for e]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7779 proof of bounds for e], id=7779<sup><span style="color:red;">new!</span></sup> -- WP guess: [[proof of bounds for e]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=9328 values of (1 + 1/n)^n for 0 &lt; n &lt; 26], id=9328<sup><span style="color:red;">new!</span></sup> -- WP guess: [[values of (1 + 1/n)^n for 0 &lt; n &lt; 26]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=9401 values of \displaystyle \sum_{i = 0}^n \frac{1}{i!} for 0 &lt; n &lt; 26], id=9401<sup><span style="color:red;">new!</span></sup> -- WP guess: [[values of \displaystyle \sum_i = 0^n \frac1i! for 0 &lt; n &lt; 26]] -- Status:

==33Bxx Elementary classical functions==

==33C05 Classical hypergeometric functions, $ 2F 1$==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6409 hypergeometric equation], id=6409 -- WP: [[hypergeometric differential equation]] -- Status: '''A'''
::[[User:Linas|linas]] 22:12, 13 Mar 2005 (UTC)
::[[User:Linas|linas]] 16:52, 26 Mar 2005 (UTC)
::I wrote the WP article a while ago, from scratch. [[User:Linas|linas]] 05:03, 22 August 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=5983 hypergeometric function], id=5983 -- WP: [[hypergeometric function]] -- Status: '''A'''
::[[User:Linas|linas]] 16:21, 13 Mar 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6150 integral representations of the hypergeometric function], id=6150 -- WP: [[Euler hypergeometric integral]] -- Status: '''A'''
::[[User:Linas|linas]] 22:16, 13 Mar 2005 (UTC)
::[[User:Linas|linas]] 16:52, 26 Mar 2005 (UTC)
::[[User:Linas|linas]] 05:05, 22 August 2005 (UTC)
::OK, the contents finally actually registered; the WP article is adequate, and the proof in the PM article didn't need to be merged. [[User:Linas|linas]] 17:31, 5 September 2005 (UTC)

==33C10 Bessel and Airy functions, cylinder functions, $ 0F 1$==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=8774 Bessel's equation], id=8774<sup><span style="color:red;">new!</span></sup> -- WP guess: [[Bessel's equation]] -- Status:

==33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6961 Legendre polynomial], id=6961 -- WP: [[Legendre polynomial]] -- Status: '''A'''
::[[User:Linas|linas]] 20:22, 5 March 2006 (UTC)

==33Cxx Hypergeometric functions==

==33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=1220 orthogonal polynomials], id=1220 -- WP: [[orthogonal polynomials]] -- Status: '''A'''
::[[User:Linas|linas]] 20:31, 13 Mar 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=8474 Christoffel-Darboux formula], id=8474<sup><span style="color:red;">new!</span></sup> -- WP guess: [[Christoffel-Darboux formula]] -- Status:

==33Dxx Basic hypergeometric functions==

==33E05 Elliptic functions and integrals==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6540 \wp-function], id=6540 -- WP: [[Weierstrass elliptic function]] -- Status: '''A'''
::[[User:Linas|linas]] 16:46, 13 Mar 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6263 derivation of integral represetations of Jacobi \vartheta functions], id=6263 -- WP: [[Derivation of integral represetations of Jacobi theta functions]] -- Status: '''NC'''
::This article provides a derivation/proof of a result quoted in main WP math articles. As such, I beleive it could be useful to copy this article, as it helps establish the correctness and consistency of WP math articles. However, one may also argue that such proofs are un-needed as long as the accuracy of WP articles remains unchallenged. [[User:Linas|linas]] 16:38, 26 Mar 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4494 elliptic function], id=4494 -- WP: [[elliptic function]] -- Status: '''A'''
::[[User:Linas|linas]] 16:43, 13 Mar 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4746 elliptic integrals and Jacobi elliptic functions], id=4746 -- WP: [[elliptic integral]] and [[Jacobian elliptic functions]] -- Status: '''A'''
::[[User:Linas|linas]] 17:13, 13 Mar 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4649 examples of elliptic functions], id=4649 -- WP: [[examples of elliptic functions]] -- Status: '''N'''
::[[User:Linas|linas]] 17:02, 13 Mar 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6262 integral represetations of Jacobi \vartheta functions], id=6262 -- WP: [[theta function]] -- Status: '''M'''
::[[User:Linas|linas]] 01:00, 14 Mar 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=5550 Jacobi \vartheta functions], id=5550 -- WP: [[theta function]] -- Status:  '''M'''
::[[User:Linas|linas]] 17:18, 13 Mar 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6427 Jacobi's identity for \vartheta functions], id=6427 -- WP: [[theta functions]] -- Status: '''M'''
::[[User:Linas|linas]] 00:06, 14 Mar 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4651 modular discriminant], id=4651 -- WP: [[modular discriminant]] -- Status: '''A'''
::[[User:Linas|linas]] 20:06, 13 Mar 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6546 product representations of Jacobi \vartheta functions], id=6546 -- WP: [[theta function]] -- Status: '''M'''
::[[User:Linas|linas]] 23:31, 13 Mar 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6434 proof of Jacobi's identity for \vartheta functions], id=6434 -- WP: [[proof of Jacobi's identity for theta functions]] -- Status: '''NC'''
::This article provides a derivation/proof of a result quoted in main WP math articles. As such, I beleive it could be useful to copy this article, as it helps establish the correctness and consistency of WP math articles. However, one may also argue that such proofs are un-needed as long as the accuracy of WP articles remains unchallenged. [[User:Linas|linas]] 16:38, 26 Mar 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4650 Weierstrass sigma function], id=4650 -- WP: [[Weierstrass sigma function]] -- Status: '''C'''
::[[User:Linas|linas]] 17:05, 13 Mar 2005 (UTC)
::Copied it over. Ugh raw tex to html conversion was needed ugh.[[User:Linas|linas]]

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7694 order of an elliptic function], id=7694<sup><span style="color:red;">new!</span></sup> -- WP guess: [[order of an elliptic function]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7772 possible orders of elliptic functions], id=7772<sup><span style="color:red;">new!</span></sup> -- WP guess: [[possible orders of elliptic functions]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=8610 reduction of elliptic integrals to standard form], id=8610<sup><span style="color:red;">new!</span></sup> -- WP guess: [[reduction of elliptic integrals to standard form]] -- Status:

==33E12 Mittag-Leffler functions and generalizations==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6594 Mittag-Leffler function], id=6594 -- WP: [[Mittag-Leffler function]] -- Status: '''C'''
::[[User:Linas|linas]] 16:26, 13 Mar 2005 (UTC)
::I just copied it over,also added the relationship to error function. [[User:Linas|linas]] 00:34, 14 Mar 2005 (UTC)

==33E20 Other functions defined by series and integrals==

==33E30 Other functions coming from differential, difference and integral equations==

==33Exx Other special functions==

==33F99 Miscellaneous==

==33Fxx Computational aspects==