Communications in Mathematical Physics

, Volume 188, Issue 2, pp 467–497

Confluent Hypergeometric Orthogonal Polynomials Related to the Rational Quantum Calogero System with Harmonic Confinement

  • J. F. van Diejen

DOI: 10.1007/s002200050174

Cite this article as:
van Diejen, J. Comm Math Phys (1997) 188: 467. doi:10.1007/s002200050174

Abstract:

Two families (type A and type B) of confluent hypergeometric polynomials in several variables are studied. We describe the orthogonality properties, differential equations, and Pieri-type recurrence formulas for these families. In the one-variable case, the polynomials in question reduce to the Hermite polynomials (type A) and the Laguerre polynomials (type B), respectively. The multivariable confluent hypergeometric families considered here may be used to diagonalize the rational quantum Calogero models with harmonic confinement (for the classical root systems) and are closely connected to the (symmetric) generalized spherical harmonics investigated by Dunkl.

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • J. F. van Diejen
    • 1
  1. 1.Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal (Québec), H3C 3J7 CanadaCA