A Comprehensive Study of Generalized Bivariate q-Laguerre Polynomials: Structural Properties and Applications

In this paper, utilizing zeroth-order q-Bessel Tricomi functions, we introduce the generalized bivariate q-Laguerre polynomials. Then, we establish the generalized bivariate q-Laguerre polynomials from the context of quasi-monomiality. We examine some of their properties, such as q-multiplicative operator property, q-derivative operator property and two q-integro-differential equations. Additionally, we derive operational representations and three q-partial differential equations for the generalized bivariate q-Laguerre polynomials. Moreover, we draw the zeros of the new polynomials, forming 2D and 3D structures, and provide a table including approximate zeros of the generalized bivariate q-Laguerre polynomials.