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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| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2017
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148580 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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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irk-123456789-1485802019-02-19T01:29:12Z Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials Odake, S. Sasaki, R. 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. 2017 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/148580 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Odake, S. Sasaki, R. |
| spellingShingle |
Odake, S. Sasaki, R. Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Odake, S. Sasaki, R. |
| author_sort |
Odake, S. |
| title |
Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials |
| title_short |
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_sort |
simplified expressions of the multi-indexed laguerre and jacobi polynomials |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148580 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT odakes simplifiedexpressionsofthemultiindexedlaguerreandjacobipolynomials AT sasakir simplifiedexpressionsofthemultiindexedlaguerreandjacobipolynomials |
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2023-05-20T17:30:10Z |
| last_indexed |
2023-05-20T17:30:10Z |
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1796153440103038976 |