Limits of elliptic hypergeometric biorthogonal functions
arXiv:1110.1456 · doi:10.1016/j.jat.2014.06.009
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.
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) elliptic hypergeometric biorthogonal functions and their measures
References in corpus (5)
- Essays on the theory of elliptic hypergeometric functions
- Duality of q-polynomials, orthogonal on countable sets of points
- Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions
- Limits of multivariate elliptic hypergeometric biorthogonal functions
- Limits of multivariate elliptic beta integrals and related bilinear forms