# Talk:Argument principle

WikiProject Mathematics (Rated Start-class, Mid-importance)
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Mathematics rating:
 Start Class
 Mid Importance
Field: Analysis

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 ${\displaystyle f(z)=e^{z}}$, ${\displaystyle g(z)=1/z}$ and ${\displaystyle C(t)=e^{2\pi it}}$ with ${\displaystyle t\in [0,2\pi ]}$ we have that ${\displaystyle {\frac {1}{2\pi i}}\oint _{C}{f'(z) \over f(z)}g(z)\,dz=1\neq 0}$ Saung Tadashi (talk) 05:16, 18 October 2014 (UTC)