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Partial differential equations having orthogonal polynomial solutions

Journal of Computational and Applied Mathematics (1998) 99(1-2) 239-253
DOI: 10.1016/S0377-0427(98)00160-5
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Abstract

We show that if a second order partial differential equation: L[u] : = Auxx + 2Buxy + Cuyy + Dux + Euy = γnu 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. © 1998 Elsevier Science B.V. All rights reserved.

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Kim, Y. J., Kwon, K. H., & Lee, J. K. (1998). Partial differential equations having orthogonal polynomial solutions. Journal of Computational and Applied Mathematics, 99(1–2), 239–253. https://doi.org/10.1016/S0377-0427(98)00160-5

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