Talk:Argument principle

The formula at the end of the chapter about the difference between a sum and integral needs citation or proof. Also, the choice for g and f should be given explicitly so that readers can follow the direction of the proof without undue time and effort. Rpchase 06:24, 18 December 2006 (UTC)


 * No big deal

Does anyone mind if we change the N in the formula to a Z. I don't think there are any conventions that will cause confusion with this. I'll leave it to the author to decide but i think most people who use this page just need a quick reference for a proof they're working on and could benifit from it being a Z.--Gtg207u 20:25, 18 April 2007 (UTC)

The date 1974 cited in History does not seem right.--lhf

Am I correct in thinking that the second last line of the introduction should read: "as the total change in the argument of f(z) as z travels around C, multiplied by i (hence the name of the theorem)" Monsterman222 (talk) 20:49, 13 December 2011 (UTC)

Cleanup section
The history section could use some cleanup. Paragraph breaks are a must, and it reads like someone summarizing a book (not very authoritative). Silly rabbit 20:11, 13 May 2007 (UTC)

Generalization
Does this generalization require g to be holomorphic? I don't have a reference handy, but it seems like a sufficient case, and it does not seem obvious (or true) that this holds when g is not holomorphic. Also, it should specifically say then the "poles of f" and the "zeroes of f". — Preceding unsigned comment added by 173.219.150.136 (talk) 02:54, 17 October 2014 (UTC)


 * I believe you're right. If $$f(z)=e^{z}$$, $$g(z)=1/z$$ and $$C(t)=e^{2\pi i t}$$ with $$t\in[0,2\pi]$$ we have that  $$\frac{1}{2\pi i}\oint_{C} {f'(z) \over f(z)} g(z) \, dz = 1 \ne 0 $$ Saung Tadashi (talk) 05:16, 18 October 2014 (UTC)