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Commun. Korean Math. Soc. 2023; 38(4): 1175-1189
Online first article October 17, 2023 Printed October 31, 2023
https://doi.org/10.4134/CKMS.c230045
Copyright © The Korean Mathematical Society.
Formulas and relations for Bernoulli-type numbers and polynomials derive from Bessel function
Selin Selen OZBEK SIMSEK, Yilmaz SIMSEK
Altinbas University; Faculty of Science Akdeniz University
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 Fa \`{a} 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.
Keywords: Bessel functions, Bernoulli numbers and polynomials, Euler numbers and polynomials, Euler gamma functions
MSC numbers: Primary 33C10, 33B10, 33B15, 11B68
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