CaltechAUTHORS
  A Caltech Library Service

Limits of multivariate elliptic hypergeometric biorthogonal functions

van de Bult, Fokko J. and Rains, Eric M. (2011) Limits of multivariate elliptic hypergeometric biorthogonal functions. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170922-152223616

[img] PDF - Submitted Version
See Usage Policy.

383Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20170922-152223616

Abstract

In this article we extend the results of our article "Limits of elliptic hypergeometric biorthogonal functions" to the multivariate setting. In that article we determined which families of biorthogonal functions arise as limits from the elliptic hypergeometric biorthogonal functions from Spiridonov when p → 0. Here we show that the classification of the possible limits of the BC_n type multivariate biorthogonal functions previously introduced by the second author is identical to the univariate classification. That is, for each univariate limit family there exists a multivariate extension, and in particular we obtain multivariate versions for all elements of the q-Askey scheme. For the Askey-Wilson polynomials these are the Koornwinder polynomials, and the multivariate versions of the Pastro polynomials form a two-parameter family which include the Macdonald polynomials.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1110.1458arXivDiscussion Paper
Record Number:CaltechAUTHORS:20170922-152223616
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170922-152223616
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81775
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:22 Sep 2017 22:31
Last Modified:22 Sep 2017 22:31

Repository Staff Only: item control page