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Orthogonal Basic Hypergeometric Laurent Polynomials
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8, випуск за цей рік
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Orthogonal Basic Hypergeometric Laurent Polynomials
Інший ID:
2010 Mathematics Subject Classification: 33D45
DOI: http://dx.doi.org/10.3842/SIGMA.2012.092
DOI: http://dx.doi.org/10.3842/SIGMA.2012.092
Посилання:
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.
Підтримка:
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.
Дата:
2012
Переглядів:
458
Завантажень:
218
Анотація:
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.
