Limits of elliptic hypergeometric biorthogonal functions

Details Limits of elliptic hypergeometric biorthogonal functions Limits of elliptic hypergeometric biorthogonal functions

2011-10-07

arxiv.org/abs/1110.1456v1

Mathematics

Classical Analysis and ODEs

27 pages. This is a self-contained article which can also be seen as part 1 of a 3 part series on limits of (multivariate) ell

Scientific paper

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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