2001/05/11 by Jasper V. Stokman, Stokman, Jasper V.
Mathematics · #33D45 #33D80 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Quantum Algebra (math.QA) #math.CA #math.QA #msc:33D45 #msc:33D80
paper · pdf · doi:10.48550/arxiv.math/0105093
24 pages. Some remarks added in section 6 on the connection with moment problems
openalex publication_date 2001/05/11 · arxiv created 2001/05/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.