Some connection and linearization problems for polynomials in and beyond the Askey scheme
| Autor: | Jorge Sánchez-Ruiz, Jesús S. Dehesa |
|---|---|
| Rok vydání: | 2001 |
| Předmět: |
Matemáticas
Orthogonal polynomials Applied Mathematics Mathematics::Classical Analysis and ODEs Mehler–Heine formula Generalized hypergeometric function Askey scheme Askey–Wilson polynomials Sobolev orthogonality Classical orthogonal polynomials Algebra Generalized hypergeometric functions Gegenbauer polynomials symbols.namesake Computational Mathematics Wilson polynomials symbols Jacobi polynomials Linearization and connection problems Mathematics |
| Zdroj: | e-Archivo. Repositorio Institucional de la Universidad Carlos III de Madrid instname |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/s0377-0427(00)00679-8 |
| Popis: | The connection problem is considered in a hypergeometric function framework for (i) the two most general families of polynomials belonging to the Askey scheme (Wilson and Racah), and (ii) some generalized Laguerre and Jacobi polynomials falling outside that scheme (Sister Celine, Cohen and Prabhakar–Jain), which are relevant to the study of quantum-mechanical systems and include as particular cases, the generalizations of the classical families with Sobolev-type orthogonality.In addition, using the same method three new linearization-like formulae for the Gegenbauer polynomials are also derived: a linearization formula that generalizes the m = n case of Dougall’s formula, the analogue of the m = n case of Nielsen’s inverse linearization formula for Hermite polynomials, and a connection formula for the squares.Closed analytical formulae for the corresponding connection and linearization coe:cients are given in terms of hypergeometric functions of unit argument, which at times can be further simpli;ed and expressed as single hypergeometric terms. c � 2001 Published by Elsevier Science B.V. |
| Databáze: | OpenAIRE |
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