Formulas for Bernoulli and Euler Numbers and Polynomials with the aid of Applications Operators and Volkenborn Integral

Year 2024, Volume: 6 Issue: 1, 41 - 58, 22.07.2024

Yılmaz Şimşek

https://doi.org/10.54286/ikjm.1476414

Abstract

Not only are there operators for studying properties for special numbers and polynomials, but the Volkenborn integral has an equally powerful applications. The aim of this article is to derive new formulas by applying operators and ($p$-adic)the Volkenborn integral to certain families polynomial, especially the Euler polynomials. These formulas include the Stirling numbers, array polynomials, the Fubini type polynomials, and the Bernoulli and Euler numbers and polynomials.

Keywords

Bernoulli numbers and polynomials, Euler numbers and polynomials, Fubini numbers and polynomials, Array numbers, Generating function, Operators, $p$-adic integral, Special functions, Stirling numbers

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