Abstract

Abstract. Two unitary integral transforms with a very-well poised 7F6-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 7F6-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. 1.

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