## The Wilson function transform

Venue: | Int. Math. Res. Not. 2003 |

Citations: | 8 - 2 self |

### BibTeX

@ARTICLE{Groenevelt_thewilson,

author = {Wolter Groenevelt},

title = {The Wilson function transform},

journal = {Int. Math. Res. Not. 2003},

year = {},

pages = {2779--2817}

}

### OpenURL

### 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.