Raising and Lowering Operators for Askey-Wilson Polynomials
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2007 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147833 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Raising and Lowering Operators for Askey-Wilson Polynomials / S. Sahi // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 25 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862720885416263680 |
|---|---|
| author | Sahi, S. |
| author_facet | Sahi, S. |
| citation_txt | Raising and Lowering Operators for Askey-Wilson Polynomials / S. Sahi // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 25 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T18:27:33Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147833 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:27:33Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Sahi, S. 2019-02-16T09:03:43Z 2019-02-16T09:03:43Z 2007 Raising and Lowering Operators for Askey-Wilson Polynomials / S. Sahi // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 25 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 33D45; 33D52; 33D80 https://nasplib.isofts.kiev.ua/handle/123456789/147833 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Raising and Lowering Operators for Askey-Wilson Polynomials Article published earlier |
| spellingShingle | Raising and Lowering Operators for Askey-Wilson Polynomials Sahi, S. |
| title | Raising and Lowering Operators for Askey-Wilson Polynomials |
| title_full | Raising and Lowering Operators for Askey-Wilson Polynomials |
| title_fullStr | Raising and Lowering Operators for Askey-Wilson Polynomials |
| title_full_unstemmed | Raising and Lowering Operators for Askey-Wilson Polynomials |
| title_short | Raising and Lowering Operators for Askey-Wilson Polynomials |
| title_sort | raising and lowering operators for askey-wilson polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147833 |
| work_keys_str_mv | AT sahis raisingandloweringoperatorsforaskeywilsonpolynomials |