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 &fnof;(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)


 * Ahlfors's discussion of Jensen's formula (in section 3.1, p. 207) uses the closed disk |z| &le; 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)

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

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)

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)


 * 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)
 * 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)