Comptes Rendus
no. 3
Number theory/Mathematical analysis
Computation and theory of Euler sums of generalized hyperharmonic numbers
the Editorial Board
Ce Xu1
1School of Mathematical Sciences, Xiamen University, Xiamen 361005, PR China
Comptes Rendus. Mathématique, Volume 356 (2018) no. 3, pp. 243-252

Recently, Dil and Boyadzhiev [10] 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.

Récemment, Dil et Boyadzhiev [10] ont établi une formule explicite pour les sommes de nombres hyper-harmoniques multiples, dont les indices sont les suites ({0}r,1). Nous montrons ici que les sommes de nombres harmoniques multiples dont les indices sont ({0}r,1;{1}k−1) peuvent être exprimées en termes de valeurs zêta (multiples), de nombres harmoniques (multiples) et de nombres de Stirling de première espèce. Nous donnons une formule explicite.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2018.01.004

Ce Xu  1

1 School of Mathematical Sciences, Xiamen University, Xiamen 361005, PR China 
Ce Xu. Computation and theory of Euler sums of generalized hyperharmonic numbers. Comptes Rendus. Mathématique, Volume 356 (2018) no. 3, pp. 243-252. doi: 10.1016/j.crma.2018.01.004
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