Some Generalizations of Spivey's Bell Number Formula

Abstract

In this paper, a generalized recurrence relation for the $r$-Whitney numbers of the second kind is derived using as framework the operators $X$ and $D$ satisfying the commutation relation $DX-XD=1$. This recurrence relation is shown to be a generalization of the well-known Spivey's Bell number. Moreover, several other identities generalizing Spivey's Bell number formula are obtained.

13 pages

Cited by in corpus (1)

• Bivariate Extension of the r-Dowling Polynomials and the Generalized Spivey's Formula