Limits of elliptic hypergeometric biorthogonal functions

To Dick Askey on the occasion of his 80th birthday

Journal article (2015)

Authors

F.J. van de Bult Analysis -

Eric M. Rains California Institute of Technology

Research Group

Analysis () (TU Delft)

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Published Date

2015

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

The purpose of this article is to bring structure to (basic) hypergeometric biorthogonal systems, in particular to the -Askey scheme of basic hypergeometric orthogonal polynomials. We aim to achieve this by looking at the limits as p -> 0 of the elliptic hypergeometric biorthogonal functions from Spiridonov (2003), with parameters which depend in varying ways on p. As a result we get 38 systems of biorthogonal functions with for each system at least one explicit measure for the bilinear form. Amongst these we indeed recover the q-Askey scheme. Each system consists of (basic hypergeometric) rational functions or polynomials.