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

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Abstract

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.

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Authors and Affiliations

  1. SISSA, Via Beirut 2-4, 34151, Trieste TS, Italy

    Martin Hallnäs

  2. Theoretical Physics, KTH, 106 91, Stockholm, Sweden

    Edwin Langmann

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  1. Martin Hallnäs
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  2. Edwin Langmann
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Correspondence to Martin Hallnäs.

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Communicated by Erik Koelink.

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Hallnäs, M., Langmann, E. A Unified Construction of Generalized Classical Polynomials Associated with Operators of Calogero–Sutherland Type. Constr Approx 31, 309–342 (2010). https://doi.org/10.1007/s00365-009-9060-4

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  • DOI: https://doi.org/10.1007/s00365-009-9060-4

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