Open AccessRepresentations of modified type 2 degenerate poly-Bernoulli polynomials
Author(s) -
Jongkyum Kwon,
Patcharee Wongsason,
Yun-Jae Kim,
Dojin Kim
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022638
Subject(s) - mathematics , difference polynomials , degenerate energy levels , wilson polynomials , lambda , macdonald polynomials , hahn polynomials , classical orthogonal polynomials , discrete orthogonal polynomials , order (exchange) , type (biology) , combinatorics , orthogonal polynomials , pure mathematics , bernoulli polynomials , koornwinder polynomials , bernoulli number , gegenbauer polynomials , physics , ecology , finance , quantum mechanics , optics , economics , biology
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.