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Partial differential equations having orthogonal polynomial solutions

✍ Scribed by Y.J. Kim; K.H. Kwon; J.K. Lee

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
717 KB
Volume
99
Category
Article
ISSN
0377-0427

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✦ Synopsis

We show that if a second order partial differential equation:

has orthogonal polynomial solutions, then the differential operator L[.] must be symmetrizable and can not be parabolic in any nonempty open subset of the plane. We also find Rodrigues type formula for orthogonal polynomial solutions of such differential equations.

πŸ“œ SIMILAR VOLUMES

Symmetrizability of differential equatio
Symmetrizability of differential equations having orthogonal polynomial solutions
✍ K.H. Kwon; G.J. Yoon πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 568 KB

We show that if a linear differential equation of spectral type with polynomial coefficients has an orthogonal polynomial system of solutions, then the differential operator LN['] must be symmetrizable. We also give a few applications of this result.

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Partial Differential Equations and Bivariate Orthogonal Polynomials
✍ Alan L. Schwartz πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 350 KB

In 1929, S. Bochner identified the families of polynomials which are eigenfunctions of a second-order linear differential operator. What is the appropriate generalization of this result to bivariate polynomials? One approach, due to Krall and Sheffer in 1967 and pursued by others, is to determine wh