$(p, q)$-analogues of the generalized Touchard polynomials and Stirling numbers

Abstract

In this paper we introduce a $(p, q)$-deformed analogues of the generalized Touchard polynomials and Stirling numbers, the post-quantum analogues of the $q$-deformed generalized Touchard polynomials and Stirling numbers. The connection between these deformations is established. A recurrence relation for the $(p, q)$-deformed generalized Touchard polynomials is expounded, elucidating a $(p, q)$-deformation of Spivey's relation.