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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)

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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)
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Record Number:CaltechAUTHORS:20170922-152223616
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81775
Deposited By: Tony Diaz
Deposited On:22 Sep 2017 22:31
Last Modified:03 Oct 2019 18:46

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