Certain characteristics of 2-variable $q$-truncated Tricomi functions

This study defines certain properties of 2-variable $q$-truncated Tricomi functions $h_{n,q}(x,y)$, such as integral forms, generating functions and series definitions. Additionally, we present the associated 2-variable $q$-Laguerre polynomials, which we utilize to obtain higher order of 2-variable $q$-truncated Tricomi functions and examine the characteristics they possess.