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. (~
On linearization and connection coefficients for generalized Hermite polynomials
โ Scribed by Hamza Chaggara; Wolfram Koepf
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 256 KB
- Volume
- 236
- Category
- Article
- ISSN
- 0377-0427
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โฆ Synopsis
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.
๐ SIMILAR VOLUMES
In the present paper, starting from the second-order difference hypergeometric ลฝ . equation on the non-uniform lattice x s satisfied by the set of discrete hypergeo-ร 4 metric orthogonal q-polynomials p , we find analytical expressions of the expann ลฝ ลฝ .. ลฝ . sion coefficients of any q-polynomial r