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An Expansion Formula for the Askey–Wilson Function

✍ Scribed by Jasper V. Stokman

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
222 KB
Volume
114
Category
Article
ISSN
0021-9045

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✦ Synopsis

The Askey-Wilson function transform is a q-analogue of the Jacobi function transform with kernel given by an explicit non-polynomial eigenfunction of the Askey-Wilson second order q-difference operator. The kernel is called the Askey-Wilson function. In this paper an explicit expansion formula for the Askey-Wilson function in terms of Askey-Wilson polynomials is proven. With this expansion formula at hand, the image under the Askey-Wilson function transform of an Askey-Wilson polynomial multiplied by an analogue of the Gaussian is computed explicitly. As a special case of these formulas a q-analogue (in one variable) of the Macdonald-Mehta integral is obtained, for which also two alternative, direct proofs are presented.

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