Some Identities of Degenerate Bell Polynomials

Taekyun Kim, Dae San Kim, Han Young Kim and Jongkyum Kwon
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Taekyun Kim: School of Science, Xian Technological University, Xian 710021, China
Dae San Kim: Department of Mathematics, Sogang University, Seoul 121-742, Korea
Han Young Kim: Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea
Jongkyum Kwon: Department of Mathematics Education and ERI, Gyeongsang National University, Jinju 52828, Korea

Mathematics, 2020, vol. 8, issue 1, 1-8

Abstract: The new type degenerate of Bell polynomials and numbers were recently introduced, which are a degenerate version of Bell polynomials and numbers and are different from the previously introduced partially degenerate Bell polynomials and numbers. Several expressions and identities on those polynomials and numbers were obtained. In this paper, as a further investigation of the new type degenerate Bell polynomials, we derive several identities involving those degenerate Bell polynomials, Stirling numbers of the second kind and Carlitz’s degenerate Bernoulli or degenerate Euler polynomials. In addition, we obtain an identity connecting the degenerate Bell polynomials, Cauchy polynomials, Bernoulli numbers, Stirling numbers of the second kind and degenerate Stirling numbers of the second kind.

Keywords: new type degenerate Bell polynomials; degenerate Bernoulli polynomials; degenerate Euler polynomials; degenerate Cauchy polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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