Date: 02 Oct 2006

Beta integrals and the associated orthogonal polynomials

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Abstract

One reason certain definite integrals are interesting is that the integrand is the weight function for an important set of orthogonal polynomials. This is true for the beta integral and many extensions. Some of these orthogonality relations are surveyed, and a new orthogonality relation is given for a recently discovered q-extension of the beta integral.

Supported in part by NSF grant DMS-8701439, in part by a sabbatical leave from the University of Wisconsin and in part by funds from the Graduate School of the University of Wisconsin.