Talk:Lerch zeta function

The PDF S. Kanemitsu, Y. Tanigawa and H. Tsukada, A generalization of Bochner's formula, attributes the fomula below to Erdelyi (see the conclusions of that paper), however, thier formula is missing a factor of z^{-a} in front. Which formula is correct, this one or thiers?



\Phi(z,s,a)=z^{-a}\left[\Gamma(1-s)\left(-\log (z)\right)^{s-1} +\sum_{k=0}^{\infty}\zeta(s-k,a)\frac{\log^{k}(a)}{k!}\right] $$

linas 01:57, 31 January 2006 (UTC)


 * Try s = a = 1. Charles Matthews 13:19, 31 January 2006 (UTC)
 * Checked numerically for different values for s and a - it's definitely wrong without the z^-a term, and the sum appears to converge to the transcendent everywhere it claims to. I'm going to remove the veracity remark, unless someone contests again. 76.210.123.228 (talk) 05:45, 24 May 2012 (UTC)

not-explained symol
What stands $$\Psi(n)$$ (Series repr., If s is a positive integer) for? --217.80.120.235 (talk) 11:57, 30 May 2009 (UTC)

Clarification
''' s=1 is a singular/undefined point. Johnson introduces a generalised Lerch zeta function (see equation (5)) which might be what the paper mentioned (A generalization of Bochner's formula) is considering (the link given seems to be inactive). See

$$\Psi$$ is the Digamma function. Please edit as appropriate.'''

Lerch zeta-function and Lerch transcendent
After the beginning of the article, the Lerch zeta-function is mentioned only once, and all formulas are written in terms of the Lerch transcendent. Because of this, I think it would be appropriate to change the name to Lerch transcendent. K9re11 (talk) 03:30, 1 January 2015 (UTC)

Relation with Hurwitz zeta function
Zeta(s,a)= lerch (1,s,a) s cannot be negative number but it isnot clarified where a is positive ISHANBULLS (talk) 03:29, 21 March 2019 (UTC)