Linearization and connection coefficients for hypergeometric-type polynomials
✍ Scribed by P.L. Artés; J.S. Dehesa; A. Martínez-Finkelshtein; J. Sánchez-Ruiz
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 479 KB
- Volume
- 99
- Category
- Article
- ISSN
- 0377-0427
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✦ Synopsis
We consider the problem of finding closed analytical formulas for both the linearization and connection coefficients for hypergeometric-type polynomials, directly in terms of the corresponding differential equations. We illustrate the method by producing explicit formulas for Hermite polynomials. (~) 1998 Elsevier Science B.V. All rights reserved.
📜 SIMILAR VOLUMES
In the present paper, starting from the second-order difference hypergeometric Ž . equation on the non-uniform lattice x s satisfied by the set of discrete hypergeo-Ä 4 metric orthogonal q-polynomials p , we find analytical expressions of the expann Ž Ž .. Ž . sion coefficients of any q-polynomial r
We consider the problem of finding explicit formulas, recurrence relations and sign properties for both connection and linearization coefficients for generalized Hermite polynomials. Most of the computations are carried out by the computer algebra system Maple using appropriate algorithms.
Several linearization-like and connection-like formulae relating the classical Gegenbauer polynomials and their squares are obtained using a theorem of the theory of generalized hypergeometric functions. (~) 2001 Elsevier Science Ltd. All rights reserved.