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.
Ce Xu
Xiamen University
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
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