Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2017; 54(4): 1255-1280

Online first article July 7, 2017      Printed July 31, 2017

https://doi.org/10.4134/BKMS.b160528

Copyright © The Korean Mathematical Society.

Some results on parametric Euler sums

Ce Xu

Xiamen University

Abstract

In this paper we present a new family of identities for parametric Euler sums which generalize a result of David Borwein et al. \cite{BBD2008}. We then apply it to obtain a family of identities relating quadratic and cubic sums to linear sums and zeta values. Furthermore, we also evaluate several other series involving harmonic numbers and alternating harmonic numbers, and give explicit formulas.

Keywords: harmonic number, Euler sum, Riemann zeta function, Hurwitz zeta function

MSC numbers: 11M06, 11M32, 11M99