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

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 Rubinstein (Ramanujan J. 27(1): 29–42, 2012). 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.