Talk:Gamma function

Article Checklist for "Gamma function"

Workgroup category or categories	Mathematics Workgroup [Categories OK]
Article status	Developed article: complete or nearly so
Underlinked article?	Yes
Basic cleanup done?	Yes
Checklist last edited by	--AlekStos 03:50, 11 April 2007 (CDT)

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On definition

I reworked slightly the definition, as it was not clear to me when z is taken to be real and when complex. Also, perhaps it is better to avoid uniform convergence at this point (isn't it more delicate?), just give continuity for granted as it is done when we say that the function is analytic. I did not understood either _why_we use for Re(z)<0 the functional equation that was "justified" for Re(z)>0. In fact, I guess that we make a formal definition which coincides with the formerly introduced analytic continuation.--AlekStos 09:00, 11 April 2007 (CDT)

I like your change. The functional-equation formula can be taken as the definition of the gamma function of a negative number. I've no idea what it'd take to prove that it really is the analytic continuation (or whatever else is needed), but I think a rigorous derivation would probably be too technical for this article. The presentation roughly follows that given in the appendix on the gamma function in Folland, Fourier analysis and its applications, which I found very readable. Fredrik Johansson 09:39, 11 April 2007 (CDT)

Zeta function

I didn't add much here beyond the definition, but added the usual form of the Riemann zeta function (the section was blank). There is a good article on the zeta function at Wolfram Mathworld [1].