Euler-Hurwitz series and non-linear Euler sums

Abstract

In this paper we derive two expressions for the Hurwitz zeta function involving the complete Bell polynomials in the restricted case where q is a positive integer greater than 1. The arguments of the complete Bell polynomials comprise the generalised harmonic number functions. These in turn give rise to Euler-Hurwitz series which may then be used to determine identities for combinations of both linear and non-linear Euler sums.

References in corpus (2)

• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume I
• Determination of some generalised Euler sums involving the digamma function

Cited by in corpus (1)

• Euler sums and a prime numbers conundrum