Degenerate poly-Bernoulli polynomials arising from degenerate polylogarithm

Abstract

Abstract Recently, degenerate polylogarithm functions were introduced by Kim and Kim. In this paper, we introduce degenerate poly-Bernoulli polynomials by means of the degenerate polylogarithm functions and investigate some their properties. In more detail, we find certain explicit expressions for those polynomials in terms of the Carlitz degenerate Bernoulli polynomials and the degenerate Stirling numbers of the second kind. Furthermore, we obtain some expressions for differences of the degenerate poly-Bernoulli polynomials.

Keywords

• Degenerate poly-Bernoulli polynomials
• Degenerate polylogarithm