p-Adic integral on Z p $\mathbb{Z}_{p}$ associated with degenerate Bernoulli polynomials of the second kind

Abstract

Abstract In this paper, by means of p-adic Volkenborn integrals we introduce and study two different degenerate versions of Bernoulli polynomials of the second kind, namely partially and fully degenerate Bernoulli polynomials of the second kind, and also their higher-order versions. We derive several explicit expressions of those polynomials and various identities involving them.

Keywords

• Degenerate Bernoulli polynomials of the second kind
• Bernoulli polynomials of the second
• Bernoulli numbers
• Degenerate Stirling numbers
• p-Adic integral