The Wilson function transform

Abstract

Two unitary integral transforms with a very-well poised ${}_7{F}_6$-function as a kernel are given. For both integral transforms the inverse is the same as the original transform after an involution on the parameters. The ${}_7{F}_6$-function involved can be considered as a non-polynomial extension of the Wilson polynomial, and is therefore called a Wilson function. The two integral transforms are called a Wilson function transform of type I and type II. Furthermore, a few explicit transformations of hypergeometric functions are calculated, and it is shown that the Wilson function transform of type I maps a basis of orthogonal polynomials onto a similar basis of polynomials.

26 pages

References in corpus (1)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue

Cited by in corpus (8)

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• Difference Sturm--Liouville problems in the imaginary direction
• Wilson polynomials/functions and intertwining operators for the generic quantum superintegrable system on the 2-sphere
• After Plancherel formula