Asymptotic Expansions of Jacobi Polynomials for Large Values of β and of Their Zeros
Asymptotic approximations of Jacobi polynomials are given for large values of the β-parameter and of their zeros. The expansions are given in terms of Laguerre polynomials and of their zeros. The levels of accuracy of the approximations are verified by numerical examples.
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209777 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Asymptotic Expansions of Jacobi Polynomials for Large Values of β and of Their Zeros / A. Gil, J. Segura, N.M. Temme // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 4 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862620903057129472 |
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| author | Gil, A. Segura, J. Temme, N.M. |
| author_facet | Gil, A. Segura, J. Temme, N.M. |
| citation_txt | Asymptotic Expansions of Jacobi Polynomials for Large Values of β and of Their Zeros / A. Gil, J. Segura, N.M. Temme // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 4 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Asymptotic approximations of Jacobi polynomials are given for large values of the β-parameter and of their zeros. The expansions are given in terms of Laguerre polynomials and of their zeros. The levels of accuracy of the approximations are verified by numerical examples.
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| first_indexed | 2025-12-07T13:22:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209777 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T13:22:35Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Gil, A. Segura, J. Temme, N.M. 2025-11-26T12:15:09Z 2018 Asymptotic Expansions of Jacobi Polynomials for Large Values of β and of Their Zeros / A. Gil, J. Segura, N.M. Temme // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 4 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C45; 41A60; 65D20 arXiv: 1804.06749 https://nasplib.isofts.kiev.ua/handle/123456789/209777 https://doi.org/10.3842/SIGMA.2018.073 Asymptotic approximations of Jacobi polynomials are given for large values of the β-parameter and of their zeros. The expansions are given in terms of Laguerre polynomials and of their zeros. The levels of accuracy of the approximations are verified by numerical examples. The authors thank the referees for their helpful comments. This work was supported by Ministerio de Economía y Competitividad, project MTM2015-67142-P (MINECO/FEDER, UE). NMT thanks CWI, Amsterdam, for scientific support. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Asymptotic Expansions of Jacobi Polynomials for Large Values of β and of Their Zeros Article published earlier |
| spellingShingle | Asymptotic Expansions of Jacobi Polynomials for Large Values of β and of Their Zeros Gil, A. Segura, J. Temme, N.M. |
| title | Asymptotic Expansions of Jacobi Polynomials for Large Values of β and of Their Zeros |
| title_full | Asymptotic Expansions of Jacobi Polynomials for Large Values of β and of Their Zeros |
| title_fullStr | Asymptotic Expansions of Jacobi Polynomials for Large Values of β and of Their Zeros |
| title_full_unstemmed | Asymptotic Expansions of Jacobi Polynomials for Large Values of β and of Their Zeros |
| title_short | Asymptotic Expansions of Jacobi Polynomials for Large Values of β and of Their Zeros |
| title_sort | asymptotic expansions of jacobi polynomials for large values of β and of their zeros |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209777 |
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