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Some connection and linearization problems for polynomials in and beyond the Askey scheme
- Source :
- e-Archivo. Repositorio Institucional de la Universidad Carlos III de Madrid, instname
- Publication Year :
- 2001
- Publisher :
- Elsevier BV, 2001.
-
Abstract
- 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.
- Subjects :
- 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
Subjects
Details
- ISSN :
- 03770427
- Volume :
- 133
- Issue :
- 1-2
- Database :
- OpenAIRE
- Journal :
- Journal of Computational and Applied Mathematics
- Accession number :
- edsair.doi.dedup.....ca66179cb2f684342dbdbd382449c5a2
- Full Text :
- https://doi.org/10.1016/s0377-0427(00)00679-8