Some Identities Involving Derangement Polynomials and Numbers and Moments of Gamma Random Variables

الملخص EN

The problem of counting derangements was initiated by Pierre Rémond de Montmort in 1708.

A derangement is a permutation that has no fixed points, and the derangement number Dn is the number of fixed point free permutations on an n element set.

Furthermore, the derangement polynomials are natural extensions of the derangement numbers.

In this paper, we study the derangement polynomials and numbers, their connections with cosine-derangement polynomials and sine-derangement polynomials, and their applications to moments of some variants of gamma random variables.