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A Note on Some Identities of New Type Degenerate Bell Polynomials
Open AccessFeature PaperArticle

Some Identities of Degenerate Bell Polynomials

1
School of Science, Xian Technological University, Xian 710021, China
2
Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea
3
Department of Mathematics, Sogang University, Seoul 121-742, Korea
4
Department of Mathematics Education and ERI, Gyeongsang National University, Jinju 52828, Korea
*
Authors to whom correspondence should be addressed.
Mathematics 2020, 8(1), 40; https://doi.org/10.3390/math8010040
Received: 10 December 2019 / Revised: 25 December 2019 / Accepted: 26 December 2019 / Published: 1 January 2020
(This article belongs to the Special Issue Special Polynomials)
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. View Full-Text
Keywords: new type degenerate Bell polynomials; degenerate Bernoulli polynomials; degenerate Euler polynomials; degenerate Cauchy polynomials new type degenerate Bell polynomials; degenerate Bernoulli polynomials; degenerate Euler polynomials; degenerate Cauchy polynomials
MDPI and ACS Style

Kim, T.; Kim, D.S.; Kim, H.Y.; Kwon, J. Some Identities of Degenerate Bell Polynomials. Mathematics 2020, 8, 40.

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