Limits of elliptic hypergeometric biorthogonal functions: To Dick Askey on the occasion of his 80th birthday

Fokko J van de Bult, Eric M. Rains

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)128-163
Number of pages36
JournalJournal of Approximation Theory
Volume193
DOIs
Publication statusPublished - 2015

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