# Voros onde dimensional zeta function

in the paper http://arxiv.org/pdf/math-ph/0005029v2.pdf formula 23 Voros evaluate and get the following spectral theta /(semiclassical) function

$\sum (E_{n}+\lambda )^{-s}= \frac{\Gamma (s-1/2)}{\Gamma(s)\sqrt \pi}\int_{0}^{\infty}\frac{dx}{(V(x)+\lambda)^{s-1/2})}= \zeta (s, \lambda)$

$H=p^{2}+V(x).$

i believe he has used the identity for the Gamma function $\Gamma (s-1/2)a^{1/2-s} = \int_{0}^{\infty} dt t^{s-1/2}e^{-at}$

However how could i compute the derivative $\frac{ \partial }{\partial s}\zeta (s, \lambda)$ at $s=0$ should i ignore all the divergent termes and simply take the finite part ?? thanks.

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