An expansion formula for the Askey-Wilson function
| dc.creator | Stokman, Jasper V. | |
| dc.date | 2001-05-11 | |
| dc.date | 2001-05-17 | |
| dc.date.accessioned | 2026-07-07T04:41:39Z | |
| dc.date.available | 2026-07-07T04:41:39Z | |
| dc.description | 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. | |
| dc.description | 24 pages. Some remarks added in section 6 on the connection with moment problems | |
| dc.identifier | https://arxiv.org/abs/math/0105093 | |
| dc.identifier | http://arxiv.org/abs/math/0105093 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61450 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Quantum Algebra | |
| dc.subject | 33D45; 33D80 | |
| dc.title | An expansion formula for the Askey-Wilson function | |
| dc.type | text |