Orthogonality of Jacobi polynomials with general parameters.
In this paper we study the orthogonality conditions satisfied by Jacobi polynomials $P_n^{(\alpha,\beta)}$ when the parameters $\alpha$ and $\beta$ are not necessarily $>-1$. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to ei...
| Main Authors: | , , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
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2012
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10835/1636 |
| _version_ | 1789406514009604096 |
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| author | Kuijlaars, A. B. J. Martínez-Finkelshtein, Andrei Orive, R. |
| author_facet | Kuijlaars, A. B. J. Martínez-Finkelshtein, Andrei Orive, R. |
| author_sort | Kuijlaars, A. B. J. |
| collection | DSpace |
| description | In this paper we study the orthogonality conditions satisfied by Jacobi polynomials $P_n^{(\alpha,\beta)}$ when the parameters $\alpha$ and $\beta$ are not necessarily $>-1$. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to either full orthogonality conditions on a single contour in the plane, or to multiple orthogonality conditions on a number of contours in the plane. In all cases we show that the orthogonality conditions characterize the Jacobi polynomial $P_n^{(\alpha, \beta)}$ of degree $n$ up to a constant factor. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-1636 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-16362023-04-12T19:38:01Z Orthogonality of Jacobi polynomials with general parameters. Kuijlaars, A. B. J. Martínez-Finkelshtein, Andrei Orive, R. Polinomios ortogonales Polinomios de Jacobi In this paper we study the orthogonality conditions satisfied by Jacobi polynomials $P_n^{(\alpha,\beta)}$ when the parameters $\alpha$ and $\beta$ are not necessarily $>-1$. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to either full orthogonality conditions on a single contour in the plane, or to multiple orthogonality conditions on a number of contours in the plane. In all cases we show that the orthogonality conditions characterize the Jacobi polynomial $P_n^{(\alpha, \beta)}$ of degree $n$ up to a constant factor. 2012-08-03T08:26:58Z 2012-08-03T08:26:58Z 2005 info:eu-repo/semantics/article 1068-9613 http://hdl.handle.net/10835/1636 en info:eu-repo/semantics/openAccess Electronic Transfer Numerical Analysis. Vol. 19, 1-17 (2005) |
| spellingShingle | Polinomios ortogonales Polinomios de Jacobi Kuijlaars, A. B. J. Martínez-Finkelshtein, Andrei Orive, R. Orthogonality of Jacobi polynomials with general parameters. |
| title | Orthogonality of Jacobi polynomials with general parameters. |
| title_full | Orthogonality of Jacobi polynomials with general parameters. |
| title_fullStr | Orthogonality of Jacobi polynomials with general parameters. |
| title_full_unstemmed | Orthogonality of Jacobi polynomials with general parameters. |
| title_short | Orthogonality of Jacobi polynomials with general parameters. |
| title_sort | orthogonality of jacobi polynomials with general parameters. |
| topic | Polinomios ortogonales Polinomios de Jacobi |
| url | http://hdl.handle.net/10835/1636 |
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