A new perspective on generalized Laguerre polynomials

Abstract This article introduces two-variable polynomials constructed with generalized Laguerre polynomials. The study focuses on deriving generating function relationships, establishing closed-form summation formulas, and proving a symmetry identity for the proposed polynomials. In addition, a theorem concerning bilinear and bilateral generating functions is rigorously established. The connections between the newly defined polynomials and other well-known polynomial families are also explored, highlighting their potential to unify and extend existing mathematical frameworks. These findings provide a comprehensive perspective on the theoretical significance and applicability of the proposed polynomials in advanced mathematical research.