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dc.contributor.author |
Mourad E.H. Ismail |
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dc.contributor.author |
Stanton, D. |
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dc.date.accessioned |
2019-02-18T17:43:17Z |
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dc.date.available |
2019-02-18T17:43:17Z |
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dc.date.issued |
2012 |
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dc.identifier.citation |
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. |
uk_UA |
dc.identifier.issn |
1815-0659 |
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dc.identifier.other |
2010 Mathematics Subject Classification: 33D45 |
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dc.identifier.other |
DOI: http://dx.doi.org/10.3842/SIGMA.2012.092 |
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dc.identifier.uri |
http://dspace.nbuv.gov.ua/handle/123456789/148664 |
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dc.description.abstract |
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. |
uk_UA |
dc.description.sponsorship |
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. |
uk_UA |
dc.language.iso |
en |
uk_UA |
dc.publisher |
Інститут математики НАН України |
uk_UA |
dc.relation.ispartof |
Symmetry, Integrability and Geometry: Methods and Applications |
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dc.title |
Orthogonal Basic Hypergeometric Laurent Polynomials |
uk_UA |
dc.type |
Article |
uk_UA |
dc.status |
published earlier |
uk_UA |
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