Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials

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For a two-parameter family of lower triangular matrices with entries involving Jacobi polynomials an explicit inverse is given, with entries involving a sum of two Jacobi polynomials. The formula simplifies in the Gegenbauer case and then one choice of the parameter solves an open problem in a recen...

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Autores principales: Cagliero, Leandro Roberto, Koornwinder, Tom H.
Formato: article
Lenguaje:Inglés
Publicado: 2021
Materias:
Jacobi polynomials
Gegenbauer polynomials
Inverses of explicit lower triangular matrices
Biorthogonal systems
Askey–Wilson polynomials
Connection coefficients
Acceso en línea:http://hdl.handle.net/11086/20820
https://doi.org/10.1016/j.jat.2014.03.016
Aporte de:
Repositorio Digital Universitario (UNC) de Universidad Nacional de Córdoba
id I10-R14111086-20820
record_format dspace
institution Universidad Nacional de Córdoba
institution_str I-10
repository_str R-141
collection Repositorio Digital Universitario (UNC)
language Inglés
topic Jacobi polynomials
Gegenbauer polynomials
Inverses of explicit lower triangular matrices
Biorthogonal systems
Askey–Wilson polynomials
Connection coefficients
spellingShingle Jacobi polynomials
Gegenbauer polynomials
Inverses of explicit lower triangular matrices
Biorthogonal systems
Askey–Wilson polynomials
Connection coefficients
Cagliero, Leandro Roberto
Koornwinder, Tom H.
Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials
topic_facet Jacobi polynomials
Gegenbauer polynomials
Inverses of explicit lower triangular matrices
Biorthogonal systems
Askey–Wilson polynomials
Connection coefficients
description For a two-parameter family of lower triangular matrices with entries involving Jacobi polynomials an explicit inverse is given, with entries involving a sum of two Jacobi polynomials. The formula simplifies in the Gegenbauer case and then one choice of the parameter solves an open problem in a recent paper by Koelink, van Pruijssen & Roman. The two-parameter family is closely related to two two-parameter groups of lower triangular matrices, of which we also give the explicit generators. Another family of pairs of mutually inverse lower triangular matrices with entries involving Jacobi polynomials, unrelated to the family just mentioned, was given by J. Koekoek & R. Koekoek (1999). We show that this last family is a limit case of a pair of connection relations between Askey–Wilson polynomials having one of their four parameters in common.
format article
author Cagliero, Leandro Roberto
Koornwinder, Tom H.
author_facet Cagliero, Leandro Roberto
Koornwinder, Tom H.
author_sort Cagliero, Leandro Roberto
title Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials
title_short Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials
title_full Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials
title_fullStr Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials
title_full_unstemmed Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials
title_sort explicit matrix inverses for lower triangular matrices with entries involving jacobi polynomials
publishDate 2021
url http://hdl.handle.net/11086/20820
https://doi.org/10.1016/j.jat.2014.03.016
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AT koornwindertomh explicitmatrixinversesforlowertriangularmatriceswithentriesinvolvingjacobipolynomials
bdutipo_str Repositorios
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