Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials
The multi-indexed Laguerre and Jacobi polynomials form a complete set of orthogonal polynomials. They satisfy second-order differential equations but not three term recurrence relations, because of the 'holes' in their degrees. The multi-indexed Laguerre and Jacobi polynomials have Wronski...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2017 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2017
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148580 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials / S. Odake, R. Sasaki // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 24 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862703298835906560 |
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| author | Odake, S. Sasaki, R. |
| author_facet | Odake, S. Sasaki, R. |
| citation_txt | Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials / S. Odake, R. Sasaki // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 24 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The multi-indexed Laguerre and Jacobi polynomials form a complete set of orthogonal polynomials. They satisfy second-order differential equations but not three term recurrence relations, because of the 'holes' in their degrees. The multi-indexed Laguerre and Jacobi polynomials have Wronskian expressions originating from multiple Darboux transformations. For the ease of applications, two different forms of simplified expressions of the multi-indexed Laguerre and Jacobi polynomials are derived based on various identities. The parity transformation property of the multi-indexed Jacobi polynomials is derived based on that of the Jacobi polynomial.
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| first_indexed | 2025-12-07T16:48:01Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148580 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:48:01Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Odake, S. Sasaki, R. 2019-02-18T16:12:55Z 2019-02-18T16:12:55Z 2017 Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials / S. Odake, R. Sasaki // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 24 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 42C05; 33C45; 34A05 DOI:10.3842/SIGMA.2017.020 https://nasplib.isofts.kiev.ua/handle/123456789/148580 The multi-indexed Laguerre and Jacobi polynomials form a complete set of orthogonal polynomials. They satisfy second-order differential equations but not three term recurrence relations, because of the 'holes' in their degrees. The multi-indexed Laguerre and Jacobi polynomials have Wronskian expressions originating from multiple Darboux transformations. For the ease of applications, two different forms of simplified expressions of the multi-indexed Laguerre and Jacobi polynomials are derived based on various identities. The parity transformation property of the multi-indexed Jacobi polynomials is derived based on that of the Jacobi polynomial. S.O. is supported in part by Grant-in-Aid for Scientific Research from the Ministry of Education,
 Culture, Sports, Science and Technology (MEXT), No. 25400395. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials Article published earlier |
| spellingShingle | Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials Odake, S. Sasaki, R. |
| title | Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials |
| title_full | Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials |
| title_fullStr | Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials |
| title_full_unstemmed | Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials |
| title_short | Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials |
| title_sort | simplified expressions of the multi-indexed laguerre and jacobi polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148580 |
| work_keys_str_mv | AT odakes simplifiedexpressionsofthemultiindexedlaguerreandjacobipolynomials AT sasakir simplifiedexpressionsofthemultiindexedlaguerreandjacobipolynomials |