Type 2 degenerate modified poly-Bernoulli polynomials arising from the degenerate poly-exponential functions

• Published in: AIMS mathematics Vol. 7; no. 6; pp. 9716 - 9730
• Main Authors: Kim, Dojin, Wongsason, Patcharee, Kwon, Jongkyum
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2022
• Subjects: degenerate poly-bernoulli polynomials; degenerate polyexponential functions; degenerate unipoly functions
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2022541

We present a new type of degenerate poly-Bernoulli polynomials and numbers by modifying the polyexponential function in terms of the degenerate exponential functions and degenerate logarithm functions. Also, we introduce a new variation of the degenerate unipoly-Bernoulli polynomials by the similar modification. Based on these polynomials, we investigate some properties, new identities, and their relations to the known special functions and numbers such as the degenerate type 2-Bernoulli polynomials, the type 2 degenerate Euler polynomials, the degenerate Bernoulli polynomials and numbers, the degenerate Stirling numbers of the first kind, and $ \lambda $-falling factorial sequence. In addition, we compute some of the proposed polynomials and present their zeros and behaviors for different variables in specific cases.