Quadratic transformations for orthogonal polynomials in one and two variables

Open Access
Authors
Publication date 2018
Host editors
  • H. Konno
  • H. Sakai
  • J. Shiraishi
  • T. Suzuki
  • Y. Yamada
Book title Representation Theory, Special Functions and Painlevé Equations — RIMS 2015
ISBN
  • 9784864970501
ISBN (electronic)
  • 9784864970518
Series Advanced Studies in Pure Mathematics
Event Representation Theory, Special Functions and Painlevé Equations - RIMS 2015
Pages (from-to) 419-447
Publisher Tokyo: Mathematical society of Japan
Organisations
  • Faculty of Science (FNWI) - Korteweg-de Vries Institute for Mathematics (KdVI)
Abstract We discuss quadratic transformations for orthogonal polynomials in one and two variables. In the one-variable case we list many (or all) quadratic transformations between families in the Askey scheme or q-Askey scheme. In the two-variable case we focus, after some generalities, on the polynomials associated with root system BC2, i.e., BC2-type Jacobi polynomials if q=1 and Koornwinder polynomials in two variables in the q-case.
Document type Conference contribution
Language English
Published at https://doi.org/10.2969/aspm/07610419
Published at https://arxiv.org/abs/1512.09294
Other links https://projecteuclid.org/euclid.aspm/1537499417
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