Orthogonal Basic Hypergeometric Laurent Polynomials

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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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dc.contributor.author	Mourad E.H. Ismail
dc.contributor.author	Stanton, D.
dc.date.accessioned	2019-02-18T17:43:17Z
dc.date.available	2019-02-18T17:43:17Z
dc.date.issued	2012
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
dc.identifier.other	2010 Mathematics Subject Classification: 33D45
dc.identifier.other	DOI: http://dx.doi.org/10.3842/SIGMA.2012.092
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/148664
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
dc.title	Orthogonal Basic Hypergeometric Laurent Polynomials	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA