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. (~
Linearization and connection coefficients of orthogonal polynomials
β Scribed by Ryszard Szwarc
- Publisher
- Springer Vienna
- Year
- 1992
- Tongue
- English
- Weight
- 421 KB
- Volume
- 113
- Category
- Article
- ISSN
- 0026-9255
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π SIMILAR VOLUMES
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.
We give explicitly recurrence relations satisfied by the connection coefficients between two families of the classical orthogonal polynomials of a discrete variable (i.e., associated with the names of Charlier, Meixner, Krawtchouk and Hahn). Also, a recurrence relation is given for the coefficients