Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials
We present various results on the properties of the four infinite sets of the exceptional Xl polynomials discovered recently by Odake and Sasaki [Phys. Lett. B 679 (2009), 414-417; Phys. Lett. B 684 (2010), 173-176]. These Xl polynomials are global solutions of second order Fuchsian differential equ...
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| Дата: | 2011 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147992 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials / C. Ho, S. Odake, R. Sasaki // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1479922019-02-17T01:24:35Z Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials Ho, C. Odake, S. Sasaki, R. We present various results on the properties of the four infinite sets of the exceptional Xl polynomials discovered recently by Odake and Sasaki [Phys. Lett. B 679 (2009), 414-417; Phys. Lett. B 684 (2010), 173-176]. These Xl polynomials are global solutions of second order Fuchsian differential equations with l+3 regular singularities and their confluent limits. We derive equivalent but much simpler looking forms of the Xl polynomials. The other subjects discussed in detail are: factorisation of the Fuchsian differential operators, shape invariance, the forward and backward shift operations, invariant polynomial subspaces under the Fuchsian differential operators, the Gram-Schmidt orthonormalisation procedure, three term recurrence relations and the generating functions for the Xl polynomials. 2011 Article Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials / C. Ho, S. Odake, R. Sasaki // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 42C05; 33E30; 81Q05 http://dx.doi.org/10.3842/SIGMA.2011.107 http://dspace.nbuv.gov.ua/handle/123456789/147992 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 |
We present various results on the properties of the four infinite sets of the exceptional Xl polynomials discovered recently by Odake and Sasaki [Phys. Lett. B 679 (2009), 414-417; Phys. Lett. B 684 (2010), 173-176]. These Xl polynomials are global solutions of second order Fuchsian differential equations with l+3 regular singularities and their confluent limits. We derive equivalent but much simpler looking forms of the Xl polynomials. The other subjects discussed in detail are: factorisation of the Fuchsian differential operators, shape invariance, the forward and backward shift operations, invariant polynomial subspaces under the Fuchsian differential operators, the Gram-Schmidt orthonormalisation procedure, three term recurrence relations and the generating functions for the Xl polynomials. |
| format |
Article |
| author |
Ho, C. Odake, S. Sasaki, R. |
| spellingShingle |
Ho, C. Odake, S. Sasaki, R. Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Ho, C. Odake, S. Sasaki, R. |
| author_sort |
Ho, C. |
| title |
Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials |
| title_short |
Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials |
| title_full |
Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials |
| title_fullStr |
Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials |
| title_full_unstemmed |
Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials |
| title_sort |
properties of the exceptional (xl) laguerre and jacobi polynomials |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147992 |
| citation_txt |
Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials / C. Ho, S. Odake, R. Sasaki // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:28:21Z |
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