&ITp&IT-Bernoulli and geometric polynomials


KARGIN L.

INTERNATIONAL JOURNAL OF NUMBER THEORY, vol.14, no.2, pp.595-613, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.1142/s1793042118500665
  • Journal Name: INTERNATIONAL JOURNAL OF NUMBER THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.595-613
  • Keywords: p-Bernoulli polynomial, geometric polynomial, finite summation, Bernoulli polynomial, poly-Bernoulli polynomial, NUMBERS, FORMULAS
  • Akdeniz University Affiliated: Yes

Abstract

We relate geometric polynomials and p-Bernoulli polynomials with an integral representation, then obtain several properties of p-Bernoulli polynomials. These results yield new identities for Bernoulli numbers. Moreover, we evaluate a Faulhaber-type summation in terms of p-Bernoulli polynomials. Finally, we introduce poly-p-Bernoulli polynomials and numbers, then study some arithmetical and number theoretical properties of them.