Finding identities and <i>q</i> -difference equations for new classes of bivariate <i>q</i> -matrix polynomials

This article introduces 2-variable q-Hermite matrix polynomials and delves into their complex representation, unravelling specific outcomes. The exploration encompasses the derivation of insightful identities for the q-cosine and q-sine analogues of the 2-variable Hermite matrix polynomials by scrutinizing their real and imaginary components. Further, the combination of the q-Appell and 2-variable q-Hermite matrix polynomials is considered to generate the 2-variable q-Hermite–Appell matrix polynomials family. The investigation of the complex form and q-difference equations of this matrix polynomial family leads to the derivation of certain results. This study contributes to the understanding of these matrix polynomials and expands the realm of q-special functions.