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


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KARGIN L., RAHMANİ M.

QUAESTIONES MATHEMATICAE, vol.41, no.7, pp.975-983, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 7
  • Publication Date: 2018
  • Doi Number: 10.2989/16073606.2017.1418762
  • Journal Name: QUAESTIONES MATHEMATICAE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.975-983
  • Keywords: Bernoulli polynomials and Bernoulli numbers, generating functions, geometric polynomials, harmonic numbers, Stirling numbers of the first and second kind, POLYNOMIALS
  • Akdeniz University Affiliated: Yes

Abstract

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.