Results 61 to 70 of about 95 (80)

Analytic extension of hyperharmonic numbers

Online Journal of Analytic Combinatorics, 2009
We define the analytic extension of hyperharmonic numbers involving the Pochhammer symbol, gamma and digamma functions. In addition, some sum of hyperharmonic series have been calculated. Surprisingly, the Lerch transcendent appears in the closed form of the sums.
openaire   +2 more sources

Multiple hyperharmonic-star numbers

Integral Transforms and Special Functions
Wenxuan Zheng, Ying Yang
exaly   +2 more sources

On the evaluation of some series attached to skew-hyperharmonic numbers

The Ramanujan Journal
Recently, skew-hyperharmonic numbers \(\widetilde{h}_n^{(r)}\) have been introduced by \textit{L. Kargın} and \textit{M. Can} [C. R., Math., Acad. Sci. Paris 358, No. 5, 535--550 (2020; Zbl 1478.11032)], which are in all respects similar to the hyperharmonic numbers in definition \[ \widetilde{h}_n^{(r)}=\sum_{k=1}^n\widetilde{h}_k^{(r-1)}, \] having ...
Mutluer, Merve, Cicimen, Mehmet, Aytaç, Pınar   +2 more
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Some identities on degenerate hyperharmonic numbers

Georgian Mathematical Journal, 2023
Taekyun Kim, Dae San Kim
exaly  

Non-integerness of class of hyperharmonic numbers

2010
Summary: Our purpose is to establish that hyperharmonic numbers -- successive partial sums of harmonic numbers -- satisfy a non-integer property. This gives a partial answer to \textit{I. Mező}\,'s conjecture [Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Math. 50, 13--20 (2007; Zbl 1212.11035)].
Amrane, Rachid Aït, Belbachir, Hacène
openaire   +2 more sources

Euler sums of generalized alternating hyperharmonic numbers II

Ramanujan Journal, 2023
Rusen Li
exaly  

Generalized alternating hyperharmonic number sums with reciprocal binomial coefficients

Journal of Mathematical Analysis and Applications, 2021
Rusen Li
exaly  

Generalized hyperharmonic number sums with reciprocal binomial coefficients

Mathematica Slovaca, 2022
Rusen Li
exaly  

Access Suspended

Rocky Mountain Journal of Mathematics, 2021
Rusen Li
exaly  

Series Expansion and Reproducing Kernels for Hyperharmonic Functions

Journal of Mathematical Analysis and Applications, 2001
Miroslav Pavlović, Miroljub Jevtic
exaly