Raising and Lowering Operators for Askey-Wilson Polynomials
| dc.contributor.author | Sahi, S. | |
| dc.date.accessioned | 2019-02-16T09:03:43Z | |
| dc.date.available | 2019-02-16T09:03:43Z | |
| dc.date.issued | 2007 | |
| dc.description.abstract | In this paper we describe two pairs of raising/lowering operators for Askey-Wilson polynomials, which result from constructions involving very different techniques. The first technique is quite elementary, and depends only on the ''classical'' properties of these polynomials, viz. the q-difference equation and the three term recurrence. The second technique is less elementary, and involves the one-variable version of the double affine Hecke algebra. | uk_UA |
| dc.description.sponsorship | This paper is a contribution to the Vadim Kuznetsov Memorial Issue “Integrable Systems and Related Topics”. We would like to thank the (anonymous) referee for several insightful suggestions which have improved the paper considerably. The referee has also pointed out that one can give an alternative proof of formulas (17) and (18) by combining Theorem 1 with the following identity relating the operators D and D`: [(1 − q²)D`z + q²D(z + z⁻¹) − q(z + z⁻¹)D] f = (1 − q) [(e₁ − e₃) − (1 − abcd)(z + z⁻¹)] f, which holds for all symmetric Laurent polynomials. | uk_UA |
| dc.identifier.citation | Raising and Lowering Operators for Askey-Wilson Polynomials / S. Sahi // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 25 назв. — англ. | uk_UA |
| dc.identifier.issn | 1815-0659 | |
| dc.identifier.other | 2000 Mathematics Subject Classification: 33D45; 33D52; 33D80 | |
| dc.identifier.uri | https://nasplib.isofts.kiev.ua/handle/123456789/147833 | |
| 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.status | published earlier | uk_UA |
| dc.title | Raising and Lowering Operators for Askey-Wilson Polynomials | uk_UA |
| dc.type | Article | uk_UA |
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