Identities for the Hurwitz zeta function, Gamma function, and L-functions

Michael O. Rubinstein

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arXiv · 1206.1992

Identities for the Hurwitz zeta function, Gamma function, and L-functions

Michael O. Rubinstein

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Abstract

We derive several identities for the Hurwitz and Riemann zeta functions, the Gamma function, and Dirichlet $L$-functions. They involve a sequence of polynomials $α_k(s)$ whose study was initiated in an earlier paper. The expansions given here are practical and can be used for the high precision evaluation of these functions, and for deriving formulas for special values. We also present a summation formula and use it to generalize a formula of Hasse.

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Michael O. Rubinstein. 2013-06-29. Identities for the Hurwitz zeta function, Gamma function, and L-functions. https://arxiv.org/abs/1206.1992

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