Some applications of degenerate poly-Bernoulli numbers and polynomials

TL;DR

This paper explores the properties of degenerate poly-Bernoulli numbers and polynomials, deriving identities through umbral calculus and their connections with polylogarithmic functions and p-adic integrals.

Contribution

It introduces new identities and relationships for degenerate poly-Bernoulli numbers and polynomials using umbral calculus and p-adic analysis.

Findings

Derived identities for degenerate poly-Bernoulli numbers and polynomials

Connected these numbers with polylogarithmic functions

Utilized p-adic invariant integrals on Zp

Abstract

In this paper, we consider degenerate poly-Bernoulli numbers and polynomials associated with polylogarithmic function and p-adic invariant integral on Zp. By using umbral calculus, we derive some identities of those numbers and polynomials