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

2012/06/10 by Michael O. Rubinstein, Rubinstein, Michael O.
Mathematics · #11M06 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11M06

paper · pdf · doi:10.48550/arxiv.1206.1992

arxiv created 2013/06/29 · arxiv updated 2013/07/02

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.

Related

• Gamma,Psi,Bernoulli Functions via Hurwitz Zeta Function
• New identities for the family of Zeta function by using distributional representations
• Identities for the Riemann zeta function
• On the Hurwitz Zeta Function
• Bernoulli identities, zeta relations, determinant expressions, Mellin transforms, and representation of the Hurwitz numbers