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arXiv · 1110.1456

Limits of elliptic hypergeometric biorthogonal functions

Fokko J. van de Bult·Eric M. Rains
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Abstract

The purpose of this article is to bring structure to (basic) hypergeometric biorthogonal systems, in particular to the q-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, 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.

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BibTeXRIS

Fokko J. van de Bult, Eric M. Rains. 2011-10-07. Limits of elliptic hypergeometric biorthogonal functions. https://doi.org/10.1016/j.jat.2014.06.009

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