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

Mutluer M., CİCİMEN M., Aytaç P.

Ramanujan Journal, cilt.68, sa.2, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 68 Sayı: 2
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s11139-025-01196-2
  • Dergi Adı: Ramanujan Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: Dirichlet series, Euler sum, Harmonic number, Hyperharmonic number, Zeta values
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.