Comptes Rendus
no. 3
Number theory/Mathematical analysis
Computation and theory of Euler sums of generalized hyperharmonic numbers
[Théorie et calcul des sommes d'Euler des nombres hyper-harmoniques généralisés]

Présenté par : the Editorial Board

Ce Xu1
1 School of Mathematical Sciences, Xiamen University, Xiamen 361005, PR China
Comptes Rendus. Mathématique, Volume 356 (2018) no. 3, pp. 243-252.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.01.004

Ce Xu 1

1 School of Mathematical Sciences, Xiamen University, Xiamen 361005, PR China 
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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.01.004/

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