Identities for the Riemann zeta function

Details Identities for the Riemann zeta function Identities for the Riemann zeta function

2008-12-14

arxiv.org/abs/0812.2592v3

Mathematics

Number Theory

14 pages

Scientific paper

We obtain several expansions for $\zeta(s)$ involving a sequence of polynomials in $s$, denoted in this paper by $\alpha_k(s)$. 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.

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