The jacobi inversion formula

Abstract

We look for differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [−1,1] with respect to the weight function where α>−1, β>−1M≥0 and N≥0. In order to find explicit formulas for the coefficients of these differential equations we have to solve systems of equations of the form where the coefficients are independent of n. This system of equations has a unique solution given by This is a consequence of the Jacobi inversion formula which is proved in this paper.