Representations of modified type 2 degenerate poly-Bernoulli polynomials

Abstract

Research on the degenerate versions of special polynomials provides a new area, introducing the λ-analogue of special polynomials and numbers, such as λ-Sheffer polynomials. In this paper, we propose a new variant of type 2 Bernoulli polynomials and numbers by modifying a generating function. Then we derive explicit expressions and their representations that provide connections among existing λ-Sheffer polynomials. Also, we provide the explicit representations of the proposed polynomials in terms of the degenerate Lah-Bell polynomials and the higher-order degenerate derangement polynomials to confirm the presented identities.

Keywords

• degenerate polyexponential functions
• degenerate poly-bernoulli polynomials
• λ-linear functionals
• λ-sheffer sequences