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Structure relations
for orthogonal polynomials
Mourad E. H. Ismail |
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Vol. 240 (2009), No. 2, 309–319
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Abstract |
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We show how to derive structure relations for general orthogonal polynomials, that is, we find operators whose action on pn is a combination of pn and pn+1 with variable coefficients. We also provide an analogue of the string equation for general orthogonal polynomials. We explore the connection with the Toda lattice and polynomials orthogonal with respect to general exponential weights. |
Keywords
general orthogonal polynomials, Freud weights, Askey–Wilson
type polynomials, Jacobi–Toda weights
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Mathematical Subject Classification 2000
Primary: 42C05
Secondary: 33C45
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Milestones
Received: 11 May 2008
Revised: 12 December 2008
Published: 4 March 2009
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Authors |
| Mourad E. H. Ismail | |
| Department of Mathematics University of Central Florida P. O. Box 161364 Orlando, FL 32816 United States |
Department of Mathematics King Saud University Riyadh Saudi Arabia |
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