The Revisited q−Derangement Polynomials and Incomplete q−Derangement Polynomials

Abstract

In this paper, the q−derangement polynomials of the second type dψ,q (γ) and their generating function are defined. Subsequently, the incomplete q−derangement polynomials dψ,q (γ, m) and numbers dψ,q (m) are introduced and various properties are derived. Furthermore, the relationship between the incomplete q−derangement numbers and q−derangement numbers is demonstrated. © MatDer.