Inversion methods for finding differential equations for generalized Jacobi polynomials

Details Inversion methods for finding differential equations for generalized Jacobi polynomials Inversion methods for finding differential equations for generalized Jacobi polynomials

1999-08-27

arxiv.org/abs/math/9908146v1

Mathematics

Classical Analysis and ODEs

23 pages

Scientific paper

We look for differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with point masses at the endpoints of the interval of orthogonality. In order to find explicit formulas for the coefficients of these differential equations we have to solve systems of equations involving derivatives of the classical Jacobi polynomials. We show that these systems of equations have a unique solution which is given explicitly. This is a consequence of the Jacobi inversion formula which is proved in this report.

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