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Degenerate s-Extended Complete and Incomplete Lah-Bell Polynomials

Hye Kyung Kim1,*, Dae Sik Lee2
1 Department of Mathematics Education, Daegu Catholic University, Gyeongsan, 38430, Korea
2 School of Electronic and Electric Engineering, Daegu University, Gyeongsan, 38453, Korea
* Corresponding Author: Hye Kyung Kim. Email:
(This article belongs to this Special Issue: Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling)

Computer Modeling in Engineering & Sciences 2022, 131(3), 1479-1495. https://doi.org/10.32604/cmes.2022.017616

Received 26 July 2021; Accepted 26 September 2021; Issue published 19 April 2022

Abstract

Degenerate versions of special polynomials and numbers applied to social problems, physics, and applied mathematics have been studied variously in recent years. Moreover, the (s-)Lah numbers have many other interesting applications in analysis and combinatorics. In this paper, we divide two parts. We first introduce new types of both degenerate incomplete and complete s-Bell polynomials respectively and investigate some properties of them respectively. Second, we introduce the degenerate versions of complete and incomplete Lah-Bell polynomials as multivariate forms for a new type of degenerate s-extended Lah-Bell polynomials and numbers respectively. We investigate relations between these polynomials and degenerate incomplete and complete s-Bell polynomials, and derive explicit formulas for these polynomials.

Keywords

Lah-Bell numbers and polynomials; s-extended Lah-Bell numbers and polynomials; complete s-Bell polynomials; incomplete s-Bell polynomials; s-Stirling numbers of second kind

Mathematics Subject Classification: 11F20; 11B68; 11B83

Cite This Article

Kim, H. K., Lee, D. S. (2022). Degenerate s-Extended Complete and Incomplete Lah-Bell Polynomials. CMES-Computer Modeling in Engineering & Sciences, 131(3), 1479–1495.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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