Orthogonal Basic Hypergeometric Laurent Polynomials
The Askey-Wilson polynomials are orthogonal polynomials in x=cosθ, which are given as a terminating ₄∅₃ basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in z=eiθ, which are given as a sum of two terminating ₄∅₃'s. They satisfy a biorthogonality rel...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2012 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2012
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148664 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Orthogonal Basic Hypergeometric Laurent Polynomials / Mourad E.H. Ismail, D. Stanton // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862717598287790080 |
|---|---|
| author | Mourad E.H. Ismail Stanton, D. |
| author_facet | Mourad E.H. Ismail Stanton, D. |
| citation_txt | Orthogonal Basic Hypergeometric Laurent Polynomials / Mourad E.H. Ismail, D. Stanton // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The Askey-Wilson polynomials are orthogonal polynomials in x=cosθ, which are given as a terminating ₄∅₃ basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in z=eiθ, which are given as a sum of two terminating ₄∅₃'s. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single ₄∅₃'s which are Laurent polynomials in z are given, which imply the non-symmetric Askey-Wilson biorthogonality. These results include discrete orthogonality relations. They can be considered as a classical analytic study of the results for non-symmetric Askey-Wilson polynomials which were previously obtained by affine Hecke algebra techniques.
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| first_indexed | 2025-12-07T18:11:08Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148664 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:11:08Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Mourad E.H. Ismail Stanton, D. 2019-02-18T17:43:17Z 2019-02-18T17:43:17Z 2012 Orthogonal Basic Hypergeometric Laurent Polynomials / Mourad E.H. Ismail, D. Stanton // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 21 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33D45 DOI: http://dx.doi.org/10.3842/SIGMA.2012.092 https://nasplib.isofts.kiev.ua/handle/123456789/148664 The Askey-Wilson polynomials are orthogonal polynomials in x=cosθ, which are given as a terminating ₄∅₃ basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in z=eiθ, which are given as a sum of two terminating ₄∅₃'s. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single ₄∅₃'s which are Laurent polynomials in z are given, which imply the non-symmetric Askey-Wilson biorthogonality. These results include discrete orthogonality relations. They can be considered as a classical analytic study of the results for non-symmetric Askey-Wilson polynomials which were previously obtained by affine Hecke algebra techniques. This paper is a contribution to the Special Issue “Superintegrability, Exact Solvability, and Special Functions”. The full collection is available at http://www.emis.de/journals/SIGMA/SESSF2012.html.
 The research of Mourad E.H. Ismail is partially supported by Research Grants Council of Hong Kong under contracts #101410 and #101411 and by King Saud University, Riyadh through grant DSFP/MATH 01. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Orthogonal Basic Hypergeometric Laurent Polynomials Article published earlier |
| spellingShingle | Orthogonal Basic Hypergeometric Laurent Polynomials Mourad E.H. Ismail Stanton, D. |
| title | Orthogonal Basic Hypergeometric Laurent Polynomials |
| title_full | Orthogonal Basic Hypergeometric Laurent Polynomials |
| title_fullStr | Orthogonal Basic Hypergeometric Laurent Polynomials |
| title_full_unstemmed | Orthogonal Basic Hypergeometric Laurent Polynomials |
| title_short | Orthogonal Basic Hypergeometric Laurent Polynomials |
| title_sort | orthogonal basic hypergeometric laurent polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148664 |
| work_keys_str_mv | AT mouradehismail orthogonalbasichypergeometriclaurentpolynomials AT stantond orthogonalbasichypergeometriclaurentpolynomials |