Some Identities Involving Derangement Polynomials and Numbers and Moments of Gamma Random Variables. (16th December 2020) - Jang, Lee-Chae; Kim, Dae San; Kim, Taekyun; Lee, Hyunseok
Abstract : 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 D n 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.