Representations of degenerate poly-Bernoulli polynomials

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