Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials
Fil: Cagliero, Leandro Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigación y Estudios de Matemática; Argentina.
| Main Authors: | , |
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| Format: | acceptedVersion |
| Language: | eng |
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2021
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| Online Access: | http://hdl.handle.net/11086/20820 https://doi.org/10.1016/j.jat.2014.03.016 |
| _version_ | 1801215056906551296 |
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| author | Cagliero, Leandro Roberto Koornwinder, Tom H. |
| author_facet | Cagliero, Leandro Roberto Koornwinder, Tom H. |
| author_sort | Cagliero, Leandro Roberto |
| collection | Repositorio Digital Universitario |
| description | Fil: Cagliero, Leandro Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigación y Estudios de Matemática; Argentina. |
| format | acceptedVersion |
| id | rdu-unc.20820 |
| institution | Universidad Nacional de Cordoba |
| language | eng |
| publishDate | 2021 |
| record_format | dspace |
| spelling | rdu-unc.208202022-10-13T11:08:13Z Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials Cagliero, Leandro Roberto Koornwinder, Tom H. Jacobi polynomials Gegenbauer polynomials Inverses of explicit lower triangular matrices Biorthogonal systems Askey–Wilson polynomials Connection coefficients acceptedVersion Fil: Cagliero, Leandro Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigación y Estudios de Matemática; Argentina. Fil: Cagliero, Leandro Roberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Fil: Koornwinder, Tom H. University of Amsterdam. Korteweg-de Vries Institute for Mathematics; Países Bajos. 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. acceptedVersion Fil: Cagliero, Leandro Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigación y Estudios de Matemática; Argentina. Fil: Cagliero, Leandro Roberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Fil: Koornwinder, Tom H. University of Amsterdam. Korteweg-de Vries Institute for Mathematics; Países Bajos. Matemática Pura 2021-10-15T16:06:31Z 2021-10-15T16:06:31Z 2015 article Cagliero, L. R. y Koornwinder, T. H. (2015). Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials. Journal of Approximation Theory, 93, 20-38. https://doi.org/10.1016/j.jat.2014.03.016 http://hdl.handle.net/11086/20820 https://doi.org/10.1016/j.jat.2014.03.016 eng Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ Impreso; Electrónico y/o Digital ISSN 0021-9045 |
| 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 |
| title | 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_short | 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 |
| topic | Jacobi polynomials Gegenbauer polynomials Inverses of explicit lower triangular matrices Biorthogonal systems Askey–Wilson polynomials Connection coefficients |
| url | http://hdl.handle.net/11086/20820 https://doi.org/10.1016/j.jat.2014.03.016 |
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