  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.
