Parameter Derivatives of the Jacobi Polynomials with Three Variables on the Simplex

Abstract

In this paper, an attempt has been made to derive parameter derivatives of Jacobi polynomials with three variables on the simplex. They are obtained via parameter derivatives of the classical Jacobi polynomials Pn(α,β)(x) with respect to their parameters. The study is motivated by the expansions of parameter derivatives which are obtained for the classical Jacobi polynomials over the interval (−1, 1), Jacobi polynomials with two variables on the triangle and some other families of orthogonal polynomials in two variables.