TY - JOUR
T1 - Limits of elliptic hypergeometric biorthogonal functions
T2 - To Dick Askey on the occasion of his 80th birthday
AU - van de Bult, Fokko J
AU - Rains, Eric M.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
U2 - 10.1016/j.jat.2014.06.009
DO - 10.1016/j.jat.2014.06.009
M3 - Article
SN - 0021-9045
VL - 193
SP - 128
EP - 163
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
ER -