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The Ramanujan Journal

, Volume 27, Issue 1, pp 29–42 | Cite as

Identities for the Riemann zeta function

  • Michael O. Rubinstein
Article

Abstract

In this paper, we obtain several expansions for ζ(s) involving a sequence of polynomials in s, denoted by α k (s). These polynomials can be regarded as a generalization of Stirling numbers of the first kind and our identities extend some series expansions for the zeta function that are known for integer values of s. The expansions also give a different approach to the analytic continuation of the Riemann zeta function.

Keywords

Riemann zeta function Stirling numbers 

Mathematics Subject Classification

11M06 

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References

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Pure Mathematics, University of Waterloo200 University Ave WWaterlooCanada

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