Computation and theory of Euler sums of generalized hyperharmonic numbers

2017/01/11 by Xu, Ce
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1701.03723

Abstract

Recently, Dil and Boyadzhiev \citeAD2015 proved an explicit formula for the sum of multiple harmonic numbers whose indices are the sequence ( \ 0 \_r,1 ). In this paper we show that the sums of multiple harmonic numbers whose indices are the sequence ( \ 0 \_r,1;\ 1 \_k-1 ) can be expressed in terms of (multiple) zeta values, multiple harmonic numbers and Stirling numbers of the first kind, and give an explicit formula.

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