@Article{cmes.2022.017616, AUTHOR = {Hye Kyung Kim, Dae Sik Lee}, TITLE = {Degenerate s-Extended Complete and Incomplete Lah-Bell Polynomials}, JOURNAL = {Computer Modeling in Engineering \& Sciences}, VOLUME = {131}, YEAR = {2022}, NUMBER = {3}, PAGES = {1479--1495}, URL = {http://www.techscience.com/CMES/v131n3/47400}, ISSN = {1526-1506}, 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.}, DOI = {10.32604/cmes.2022.017616} }