Abstract
We introduce the theory of two-variable q-Laguerre polynomials by means of a generating function involving zeroth-order q-Bessel Tricomi functions and we establish two-variable q-Laguerre polynomials from the context of quasi-monomiality. Then we obtain the operational representations and q-integrodifferential equations for two-variable q-Laguerre polynomials. Moreover, we introduce mth-order two-variable q-Laguerre polynomials, we deduce the q-partial differential equations and q-integrodifferential equations for mth-order two-variable q-Laguerre polynomials and we also examine the quasi-monomiality characteristics of these new q-special polynomials. Finally, we give some graphical representations of q-Laguerre polynomials.
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