The Wilson function transform

Details The Wilson function transform The Wilson function transform

2003-06-30

arxiv.org/abs/math/0306424v1

Int. Math. Res. Not. 2003, no. 52, 2779--2817

Mathematics

Classical Analysis and ODEs

26 pages

Scientific paper

Two unitary integral transforms with a very-well poised $_7F_6$-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 $_7F_6$-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.

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