Asymptotics of multivariate orthogonal polynomials with hyperoctahedral symmetry

Details Asymptotics of multivariate orthogonal polynomials with hyperoctahedral symmetry Asymptotics of multivariate orthogonal polynomials with hyperoctahedral symmetry

2004-12-29

arxiv.org/abs/math/0412532v1

Contemporary Math. 417 (2006), 157-169

Mathematics

Classical Analysis and ODEs

13 pages, LaTeX

Scientific paper

We present a formula describing the asymptotics of a class of multivariate orthogonal polynomials with hyperoctahedral symmetry as the degree tends to infinity. The polynomials under consideration are characterized by a factorized weight function satisfying certain analyticity assumptions. As an application, the large-degree asymptotics of the Koornwinder-Macdonald BC_N-type multivariate Askey-Wilson polynomials is determined.

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