Representations of degenerate poly-Bernoulli polynomials

Abstract: As is well-known, poly-Bernoulli polynomials are defined in terms of polylogarithm functions. Recently, as degenerate version of such functions and polynomials, degenerate polylogarithm functions were introduced and degenertae poly-Bernoulli polynomials were defined by means of the degenerate polylogarithm functions, and some their properties were investigated. The aim of this paper is to furthur study some properties of the degenertae poly-Bernoulli polynomials by using three formulas coming from the recently developed lambda-umbral calculus. In more detail, among other things, we represent the degenerate poly-Bernoulli polynomials by higher-order degenertae Bernoulli polynomials and by higher-order degenerate derangements polynomials.