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Orthogonal polynomial solutions of even-ordered ordinary differential equations

✍ Scribed by R.G Huffstutler; R Vorheis

Book ID
107776541
Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
179 KB
Volume
7
Category
Article
ISSN
0021-9045

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πŸ“œ SIMILAR VOLUMES

Partial differential equations having or
Partial differential equations having orthogonal polynomial solutions
✍ Y.J. Kim; K.H. Kwon; J.K. Lee πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 717 KB

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

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✍ 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.