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

Dojin Kim; Patcharee Wongsason; Jongkyum Kwon; Dojin Kim; Patcharee Wongsason; Jongkyum Kwon

doi:10.3934/math.2022541

AIMS Mathematics

2022, Volume 7, Issue 6: 9716-9730. doi: 10.3934/math.2022541

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

1.
Department of Mathematics, Dongguk University, Seoul 04620, Republic of Korea
2.
Department of Mathematics, Statistics and Computers, Faculty of Sciences, Ubon Ratchathani University, Ubon Ratchathani, Thailand
3.
Department of Mathematics Education and ERI, Gyeongsang National University, Jinju 52828, Republic of Korea

Received: 06 December 2021 Revised: 05 March 2022 Accepted: 07 March 2022 Published: 16 March 2022
MSC : 05A19, 11B73, 11B83

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.
- degenerate polyexponential functions,
- degenerate poly-Bernoulli polynomials,
- degenerate unipoly functions
Citation: Dojin Kim, Patcharee Wongsason, Jongkyum Kwon. Type 2 degenerate modified poly-Bernoulli polynomials arising from the degenerate poly-exponential functions[J]. AIMS Mathematics, 2022, 7(6): 9716-9730. doi: 10.3934/math.2022541

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Abstract

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.

References

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