Some results on parametric Euler sums
Bull. Korean Math. Soc. 2017 Vol. 54, No. 4, 1255-1280
Published online July 31, 2017
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
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