Stieltjes constants appearing in the Laurent expansion of the hyperharmonic zeta function

CAN M., DİL A., KARGIN L.

Ramanujan Journal, cilt.61, sa.3, ss.873-894, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 61 Sayı: 3
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s11139-022-00676-z
  • Dergi Adı: Ramanujan Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.873-894
  • Anahtar Kelimeler: Euler sum, Harmonic numbers, Hyperharmonic numbers, Integro-exponential function, Laurent expansion, Stieltjes constant, Zeta values
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, we consider meromorphic extension of the function ζh(r)(s)=∑k=1∞hk(r)ks,Re(s)>r(which we call hyperharmonic zeta function) where hn(r) are the hyperharmonic numbers. We establish certain constants, denoted γh(r)(m), which naturally occur in the Laurent expansion of ζh(r)(s). Moreover, we show that the constants γh(r)(m) and integrals involving the generalized exponential integral can be written as a finite combination of some special constants.