Differential equations for generalized Jacobi polynomials

Details Differential equations for generalized Jacobi polynomials Differential equations for generalized Jacobi polynomials

1999-08-30

arxiv.org/abs/math/9908162v1

J. Comput. Appl. Math. 126, 2000, 1-31.

Mathematics

Classical Analysis and ODEs

33 pages, submitted for publication

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 two point masses at the endpoints of the interval of orthogonality. We show that such a differential equation is uniquely determined and we give explicit representations for the coefficients. In case of nonzero mass points the order of this differential equation is infinite, except for nonnegative integer values of (one of) the parameters. Otherwise, the finite order is explictly given in terms of the parameters.

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