The Jacobi inversion formula
Classical Analysis and ODEs
2007-05-23 v1
Abstract
We look for spectral type 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. These systems of equations have a unique solution which can be given explicitly in terms of Jacobi polynomials. This is a consequence of the Jacobi inversion formula which is proved in this paper.
Cite
@article{arxiv.math/9908148,
title = {The Jacobi inversion formula},
author = {J. Koekoek and R. Koekoek},
journal= {arXiv preprint arXiv:math/9908148},
year = {2007}
}
Comments
15 pages