Constructive Approximation

, Volume 31, Issue 3, pp 309–342

A Unified Construction of Generalized Classical Polynomials Associated with Operators of Calogero–Sutherland Type


DOI: 10.1007/s00365-009-9060-4

Cite this article as:
Hallnäs, M. & Langmann, E. Constr Approx (2010) 31: 309. doi:10.1007/s00365-009-9060-4


In this paper we consider a large class of many-variable polynomials which contains generalizations of the classical Hermite, Laguerre, Jacobi and Bessel polynomials as special cases, and which occur as the polynomial part in the eigenfunctions of Calogero–Sutherland type operators and their deformations recently found and studied by Chalykh, Feigin, Sergeev, and Veselov. We present a unified and explicit construction of all these polynomials.


Calogero–Sutherland operators Many-variable polynomials Series representations Exactly solvable quantum many-body systems 

Mathematics Subject Classification (2000)

33C70 81U15 

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.SISSATrieste TSItaly
  2. 2.Theoretical PhysicsKTHStockholmSweden

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