APPLYING NÖRLUND SUM TO BESSEL FUNCTION AND GENERATING FUNCTION FOR GENERALIZED BERNOULLI POLYNOMIALS: APPROACH TO (INVERSE) LAPLACE TRANSFORM

ŞÜKRÜOĞLU E., ŞİMŞEK Y.

Journal of Inequalities and Special Functions, vol.16, no.4, pp.10-19, 2025 (ESCI, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 4
  • Publication Date: 2025
  • Doi Number: 10.54379/jiasf-2025-4-2
  • Journal Name: Journal of Inequalities and Special Functions
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.10-19
  • Keywords: Bernoulli polynomials, Bessel function, Generating function, Laplace transform, Nörlund sum
  • Akdeniz University Affiliated: Yes

Abstract

The aim of this paper is to apply the Nörlund sum to Bessel function and generalized Bernoulli polynomials involving this function, we derive some new relations and integral formulas. By applying the Laplace transform with its inverse to generating function for the generalized Bernoulli polynomials involving the Bessel function, we also derive infinite series representation for these polynomials. Furthermore, some relationship between the Bessel function and the Nörlund sum is found. We also give some new relations by comparing specific values to the Bessel function and modified Bessel functions with the aid of their Laplace transforms by its inverse.