Representations of modified type 2 degenerate poly-Bernoulli polynomials

Abstract

<abstract><p>Research on the degenerate versions of special polynomials provides a new area, introducing the $ \lambda $-analogue of special polynomials and numbers, such as $ \lambda $-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 $ \lambda $-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.</p></abstract>