J. Koekoek, R. Koekoek
Published 1999-08-27Version 1
We find all spectral type differential equations satisfied by the symmetric generalized ultraspherical polynomials which are orthogonal on the interval [-1,1] with respect to the classical symmetric weight function for the Jacobi polynomials together with equal mass points at both ends 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 is given explicitly. This is a consequence of the Jacobi inversion formula.
Comments: 10 pages, published in Proceedings of the International Workshop on Orthogonal Polynomials in Mathematical Physics (Leganes, 1996), Universidad Carlos III Madrid (Leganes, 1997), 103-111. See also : http://dulcinea.uc3m.es/users/workshop/proceedings.html
Journal: Proceedings of the International Workshop on Orthogonal Polynomials in Mathematical Physics (Legan\'es, 1996), Universidad Carlos III Madrid, Legan\'es, 1997, 103-111.
Differential equations for symmetric generalized ultraspherical polynomials
Inversion methods for finding differential equations for generalized Jacobi polynomials
The search for differential equations for certain sets of orthogonal polynomials
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