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Open AccessArticle

A Note on Some Identities of New Type Degenerate Bell Polynomials

1
School of Science, Xi’an Technological University, Xi’an 710021, China
2
Department of Mathematics, Kwangwoon University, Seoul 01897, Korea
3
Department of Mathematics, Sogang University, Seoul 04107, Korea
4
Department of Mathematics Education and ERI, Gyeongsang National University, Gyeongsangnamdo 52828, Korea
*
Authors to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1086; https://doi.org/10.3390/math7111086
Received: 24 October 2019 / Revised: 7 November 2019 / Accepted: 7 November 2019 / Published: 11 November 2019
(This article belongs to the Special Issue Special Polynomials)
Recently, the partially degenerate Bell polynomials and numbers, which are a degenerate version of Bell polynomials and numbers, were introduced. In this paper, we consider the new type degenerate Bell polynomials and numbers, and obtain several expressions and identities on those polynomials and numbers. In more detail, we obtain an expression involving the Stirling numbers of the second kind and the generalized falling factorial sequences, Dobinski type formulas, an expression connected with the Stirling numbers of the first and second kinds, and an expression involving the Stirling polynomials of the second kind. View Full-Text
Keywords: Bell polynomials; partially degenerate Bell polynomials; new type degenerate Bell polynomials Bell polynomials; partially degenerate Bell polynomials; new type degenerate Bell polynomials
MDPI and ACS Style

Kim, T.; Kim, D.S.; Lee, H.; Kwon, J. A Note on Some Identities of New Type Degenerate Bell Polynomials. Mathematics 2019, 7, 1086.

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