Representations of modified type 2 degenerate poly-Bernoulli polynomials

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

doi:10.3934/math.2022638

AIMS Mathematics

2022, Volume 7, Issue 6: 11443-11463. doi: 10.3934/math.2022638

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Representations of modified type 2 degenerate poly-Bernoulli polynomials

1.
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Republic of Korea
2.
Department of Mathematics, Statistics and Computers, Faculty of Sciences, Ubon Ratchathani University, Ubon Ratchathani 34190, Thailand
3.
Department of Mathematics, Kyungpook National University, Daegu 41566, Republic of Korea
4.
Department of Mathematics, Dongguk University, Seoul 04620, Republic of Korea

Received: 07 January 2022 Revised: 26 March 2022 Accepted: 10 April 2022 Published: 13 April 2022
MSC : 05A19, 11B73, 11B83

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.
Citation: Jongkyum Kwon, Patcharee Wongsason, Yunjae Kim, Dojin Kim. Representations of modified type 2 degenerate poly-Bernoulli polynomials[J]. AIMS Mathematics, 2022, 7(6): 11443-11463. doi: 10.3934/math.2022638

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Abstract

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.

References

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