A closed formula for the generating function of p-Bernoulli numbers

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KARGIN L., RAHMANİ M.

QUAESTIONES MATHEMATICAE, cilt.41, sa.7, ss.975-983, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 7
  • Basım Tarihi: 2018
  • Doi Numarası: 10.2989/16073606.2017.1418762
  • Dergi Adı: QUAESTIONES MATHEMATICAE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.975-983
  • Anahtar Kelimeler: Bernoulli polynomials and Bernoulli numbers, generating functions, geometric polynomials, harmonic numbers, Stirling numbers of the first and second kind, POLYNOMIALS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, using geometric polynomials, we obtain a generating function of p-Bernoulli numbers in terms of harmonic numbers. As consequences of this generating function, we derive closed formulas for the finite summation of Bernoulli and harmonic numbers involving Stirling numbers of the second kind. We also give a relationship between the p-Bernoulli numbers and the generalized Bernoulli polynomials.