The extended jacobi polynomials in two variables: A generalization

This work presents an extension of the Jacobi polynomials to two variables and generates a number of generating functions. In addition, certain applications of Jacobi polynomials are examined, along with Bateman's and Brafman's generating functions, Rodrigues formula, and the relationship between Legendre and Jacobi polynomials. The main objective of this study is to construct and describe certain properties of an analogue of extended Jacobi polynomials that operates on two variables. The authors provide recurrence relations that use extended ϱJacobi polynomials in two variables, along with a variety of differential equations for these polynomials.