Degenerate polyexponential functions and type 2 degenerate poly-Bernoulli numbers and polynomials

• Main Authors: Taekyun Kim, Dae San Kim, Jongkyum Kwon, Hyunseok Lee
• Format: Article
• Language: English
• Published: SpringerOpen 2020-04-01
• Series: Advances in Difference Equations
• Subjects: Degenerate polyexponential functions; Type 2 degenerate poly-Bernoulli polynomials; Type 2 degenerate poly-Bernoulli numbers
• Online Access: http://link.springer.com/article/10.1186/s13662-020-02636-7

Abstract The polyexponential functions were introduced by Hardy and rediscovered by Kim, as inverses to the polylogarithm functions. Recently, the type 2 poly-Bernoulli numbers and polynomials were defined by means of the polyexponential functions. In this paper, we introduce the degenerate polyexponential functions and the degenerate type 2 poly-Bernoulli numbers and polynomials, as degenerate versions of such functions and numbers and polynomials. We derive several explicit expressions and some identities for those numbers and polynomials.