Instant Evaluation and Demystification of zeta(n),L(n,chi) that Euler,Ramanujan Missed - II

2008/07/16 by Vivek V. Rane, Rane, Vivek V.
Chemistry · Mathematics · #11M35 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #History and advancements in chemistry #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0807.2626

openalex publication_date 2008/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For Hurwitz zeta function, we obtain power series expression in second variable for its higher order derivatives (with respect to first variable) at non-positive integer arguments and consequently obtain rapidly decreasing series expression for Riemann zeta fuction at positive odd integer arguments. Further, we obtain corresponding results for Dirichlet L-series. We also a unified proof of various classical identities involving Riemann zeta values.

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