Talk:Jensen's formula

What is r?

The formula refers to a number called r without saying what it is. It also fails to indicate that 0 is in the disk D, but says ƒ(0) = ... etc.

My guess: A disk centered at 0 was intended, and r is supposed to be a positive number strictly smaller than the radius of that disk.

Right? Michael Hardy (talk) 16:07, 26 July 2009 (UTC)[reply]

Ahlfors's discussion of Jensen's formula (in section 3.1, p. 207) uses the closed disk |z| ≤ ρ, and in his statement of the formula he uses the same variable ρ. So I'd say r here is the radius of the disk, not a strictly smaller positive number. Michael Slone (talk) 17:24, 26 July 2009 (UTC)[reply]

Thank you. I should have looked in Ahlfors. Michael Hardy (talk) 22:39, 26 July 2009 (UTC)[reply]

I am not an expert or something,

but the formula seems to be some kind of generalisation of the Vieta's formula $x_{1}x_{2}\dots x_{n}=(-1)^{n}{\tfrac {a_{0}}{a_{n}}}$ for polynomials, unless I am wrong --77.125.72.170 (talk) 19:20, 9 April 2012 (UTC)[reply]

Mistake in Jensen's formula for meromorphic functions

Is the formula for meromorphic functions correct? For example for f(z)=z it seems to be false. I think the correct statement would be

\log \left|{\frac {g(0)}{h(0)}}\right|=\log \left|r^{m-n-l}{\frac {a_{1}\ldots a_{n}}{b_{1}\ldots b_{m}}}\right|+{\frac {1}{2\pi }}\int _{0}^{2\pi }\log |f(re^{i\theta })|\,d\theta .

— Preceding unsigned comment added by 141.201.164.120 (talk) 14:08, 2 September 2014 (UTC)[reply]

Indeed. Based on this simple argument, I am "boldly" making the change in the article, now. Not sure why no one has dealt with this earlier. 67.198.37.16 (talk) 04:30, 15 April 2024 (UTC)[reply]

Thank you for the edit. In this case is pretty obvious, but try to provide a reference in future. Roffaduft (talk) 06:12, 15 April 2024 (UTC)[reply]