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Raising and Lowering Operators for Askey-Wilson Polynomials

Siddhartha Sahi
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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.

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Siddhartha Sahi. 2007-01-04. Raising and Lowering Operators for Askey-Wilson Polynomials. https://doi.org/10.3842/sigma.2007.002

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