Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published May 2015 | Submitted
Journal Article Open

Limits of elliptic hypergeometric biorthogonal functions

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 (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.

Additional Information

© 2014 Elsevier Inc. Received 19 July 2013, Revised 9 June 2014, Accepted 25 June 2014, Available online 2 July 2014. Communicated by Spec. Issue Guest Editor. To Dick Askey on the occasion of his 80th birthday. We would like to thank an anonymous reviewer for insightful remarks. Eric M. Rains was partially supported by a grant from the National Science Foundation, DMS-1001645.

Attached Files

Submitted - 1110.1456v1.pdf

Files

1110.1456v1.pdf
Files (377.4 kB)
Name Size Download all
md5:89d6dd9eb62e78598f2db64c22879198
377.4 kB Preview Download

Additional details

Created:
August 20, 2023
Modified:
March 5, 2024