Some identities related to degenerate r-Bell and degenerate Fubini polynomials

Abstract

Many works have been done in recent years as to explorations for degenerate versions of some special polynomials and numbers, which began with the pioneering work of Carlitz on the degenerate Bernoulli and degenerate Euler polynomials. This paper is focused on the study of some properties, recurrence relations and identities related to the degenerate r-Bell polynomials, the two variable degenerate Fubini polynomials and the degenerate r-Stirling numbers of the second kind. Especially, we express the power series $ \sum _{n=0}^{\infty }\sum _{k=0}^{n}(k+r)_{p,\lambda }\frac {x^n}{n!} $ in terms of the degenerate r-Bell polynomials, of the degenerate r-Stirling numbers of the second kind and of the degenerate Fubini polynomials.

Keywords

• degenerate r-bell polynomials
• two variable degenerate fubini polynomials
• degenerate r-stirling numbers of the second kind