Talk:Euler function

Mathematics Stub‑class Low‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics
Stub	This article has been rated as Stub-class on Wikipedia's content assessment scale.
Low	This article has been rated as Low-priority on the project's priority scale.

Also Interesting

The cube of the Euler function, and its natural logarithm are also interesting - insofar as they both have interesting (i.e. simple) Taylor expansions anout q=0.

Perhaps these should be added to the article? Hair Commodore (talk) 14:39, 14 January 2009 (UTC)[reply]

And I forgot to add its Functional Equation! Hair Commodore (talk) 15:14, 14 January 2009 (UTC)[reply]

There is a particularly elegant derivation of the functional equation for this function - to be found in the book: Asymptotics and Mellin-Barnes Integrals, by R.B. Paris and D. Kaminski (Cambridge University Press, 2001). Hair Commodore (talk) 15:14, 12 February 2009 (UTC)[reply]

Notation: possible confusion

The use of lowercase-phi for this function is potentially confusing, especially as it is also used as standard for Euler's totient function, albeit sometimes in a different script!

One obvious alternative is to use an uppercase-E in script or italic form. Hair Commodore (talk) 12:01, 15 January 2009 (UTC)[reply]

What about this related function too?

 : $\psi (q)=\prod _{k=1}^{\infty }(1+q^{k}).$ ,

whose relationship to the Modular Group is also obvious! 81.102.15.200 (talk) 12:18, 30 June 2009 (UTC)[reply]