Jack polynomials, generalized binomial coefficients and polynomial solutions of the generalized Laplace's equation

Details Jack polynomials, generalized binomial coefficients and polynomial solutions of the generalized Laplace's equation Jack polynomials, generalized binomial coefficients and polynomial solutions of the generalized Laplace's equation

1997-10-23

arxiv.org/abs/solv-int/9710017v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

19 pages, latex, no figures, 12 tables Minor typographical errors in some of the equations and the tables have been corrected

Scientific paper

10.1142/S0217732398000772

We discuss the symmetric homogeneous polynomial solutions of the generalized Laplace's equation which arises in the context of the Calogero-Sutherland model on a line. The solutions are expressed as linear combinations of Jack polynomials and the constraints on the coefficients of expansion are derived. These constraints involve generalized binomial coefficients defined through Jack polynomials. Generalized binomial coefficients for partitions of $k$ upto $k=6$ are tabulated.

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