Euler-Hurwitz series and non-linear Euler sums
arXiv:0803.1304
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 (4)
- Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume I
- A Set of Identities for a Class of Alternating Binomial Sums Arising in Computing Applications
- Convergence acceleration of series through a variational approach
- Determination of some generalised Euler sums involving the digamma function