On the evaluation of some series attached to skew-hyperharmonic numbers
Ramanujan Journal, vol.68, no.2, 2025 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 68 Issue: 2
- Publication Date: 2025
- Doi Number: 10.1007/s11139-025-01196-2
- Journal Name: Ramanujan Journal
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Keywords: Dirichlet series, Euler sum, Harmonic number, Hyperharmonic number, Zeta values
- Akdeniz University Affiliated: Yes
Abstract
In this study, we first obtain a closed form expression for the Euler sums of skew-hyperharmonic numbers h~nr, which are defined as similar to the hyperharmonic numbers hnr in all respects. We then give a representation for the Euler-type sum of the numbers an,l1, where an,lr=h~nrn+ll-1 with h~n1=H~n, the nth skew-harmonic number. This representation enables us to show that the Euler-type sum of the numbers an,lr can be expressed in terms of zeta values and harmonic numbers. Finally, we investigate the Dirichlet-type generating functions of the numbers an,lr.