Degenerate s-Extended Complete and Incomplete Lah-Bell Polynomials

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.