Some identities involving derangement polynomials and r-Bell polynomials

Abstract

In this paper two kinds of identities involving derangement polynomials and $ r $-Bell polynomials were established. The identities of the first kind extended the identity on derangement numbers and Bell numbers due to Clarke and Sved and its generalizations due to Du and Fonseca. The identities of the second kind extended some of the results on derangement polynomials and Bell polynomials due to Kim et al.

Keywords

• derangement polynomials
• $ r $-bell polynomials
• stirling numbers
• identities