The Jacobi inversion formula

Details The Jacobi inversion formula The Jacobi inversion formula

1999-08-27

arxiv.org/abs/math/9908148v1

Complex Variables 39 (1999) 1-18

Mathematics

Classical Analysis and ODEs

15 pages

Scientific paper

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.

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