FORMULAS AND RELATIONS FOR BERNOULLI-TYPE NUMBERS AND POLYNOMIALS DERIVE FROM BESSEL FUNCTION

Simsek S. S. O., ŞİMŞEK Y.

Communications of the Korean Mathematical Society, vol.38, no.4, pp.1175-1189, 2023 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 4
  • Publication Date: 2023
  • Doi Number: 10.4134/ckms.c230045
  • Journal Name: Communications of the Korean Mathematical Society
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Page Numbers: pp.1175-1189
  • Keywords: Bernoulli numbers and polynomials, Bessel functions, Euler gamma functions, Euler numbers and polynomials
  • Akdeniz University Affiliated: Yes

Abstract

The main purpose of this paper is to give some new identities and properties related to Bernoulli type numbers and polynomials associated with the Bessel function of the first kind. We give symmetric properties of the Bernoulli type numbers and polynomials. Moreover, using generating functions and the Faà di Bruno’s formula, we derive some new formulas and relations related to not only these polynomials, but also the Bernoulli numbers and polynomials and the Euler numbers and polynomials.