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Symmetry, Integrability and Geometry: Methods and Applications, 2007, Volume 3, 002, 11 pp.
DOI: https://doi.org/10.3842/SIGMA.2007.002 (Mi sigma128) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Raising and Lowering Operators for Askey–Wilson Polynomials

S. Sahi

Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA
Full-text PDF (223 kB) Citations (8)
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DOI: https://doi.org/10.3842/SIGMA.2007.002
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.
Keywords: orthogonal polynomials; Askey–Wilson polynomials; $q$-difference equation; three term recurrence; raising operators; lowering operators; root systems; double affine Hecke algebra.
Received: September 20, 2006; in final form December 27, 2006; Published online January 4, 2007
Bibliographic databases:
Document Type: Article
MSC: 33D45; 33D52; 33D80
Language: English
Citation: S. Sahi, “Raising and Lowering Operators for Askey–Wilson Polynomials”, SIGMA, 3 (2007), 002, 11 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
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