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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2012 |
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| Zitieren: | 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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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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Orthogonal Basic Hypergeometric Laurent Polynomials |
| spellingShingle |
Orthogonal Basic Hypergeometric Laurent Polynomials Mourad E.H. Ismail Stanton, D. |
| title_short |
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_sort |
orthogonal basic hypergeometric laurent polynomials |
| author |
Mourad E.H. Ismail Stanton, D. |
| author_facet |
Mourad E.H. Ismail Stanton, D. |
| publishDate |
2012 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
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Article |
| 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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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148664 |
| 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. |
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AT mouradehismail orthogonalbasichypergeometriclaurentpolynomials AT stantond orthogonalbasichypergeometriclaurentpolynomials |
| first_indexed |
2025-12-07T18:11:08Z |
| last_indexed |
2025-12-07T18:11:08Z |
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1850874075146092544 |