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An asymptotic expansion for the first derivative of the generalized Riemann zeta-function. (English) Zbl 0603.10040
An asymptotic expansion for the partial derivative $(\partial /\partial z)\zeta (q,z)\vert\sb{z=m}$ ($m=-1, -2,...$) of the generalized Riemann zeta-function $\zeta (z,q)=\sum\sp{\infty}\sb{n=1}(n+q)\sp{-z}$ ($\text{Re}\, z>1$, $q\ne 0, -1, -2,...$) is given. The method is similar to a previous paper of the author [J. Phys. A 18, 1637--1640 (1985; Zbl 0603.10039)] but uses power series expansions of $\arctan x$ and $\log (1+x)$ instead of partial integration.
Reviewer: D.Leitmann

11M35Hurwitz and Lerch zeta functions
11M06$\zeta (s)$ and $L(s, \chi)$
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