Identities for the Riemann zeta function

Abstract

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.

14 pages

Cited by in corpus (2)

• Series representations of the Riemann and Hurwitz zeta functions and series and integral representations of the first Stieltjes constant
• Recursion Relations and Functional Equations for the Riemann Zeta Function