$q$-NATURAL TRANSFORMS OF CERTAIN $q$-HUMBERT FUNCTIONS

The ${\bf N}$-transform (so-called natural transform) of a function, which may combine Laplace and Sumudu transforms, has been introduced and investigated. Recently $q$-analogues of the ${\bf N}$-transform has been presented and studied. Among $q$-extensions of a number of polynomials and functions, the $q$-Humbert functions and some of their interesting identities and properties have recently been introduced and provided. In this paper, we aim to present $q$-natural transforms of a finite product of the $q$-Humbert functions. Some particular cases of our main identities are also considered.