On homogeneous polynomial solutions of the Riesz system and their harmonic potentials

2007 ◽  
Vol 52 (10-11) ◽  
pp. 1047-1061 ◽  
Author(s):  
R. Delanghe
Keyword(s):  
Homogeneous Polynomial ◽  
Polynomial Solutions ◽  
Riesz System

scholarly journals JACK POLYNOMIALS, GENERALIZED BINOMIAL COEFFICIENTS AND POLYNOMIAL SOLUTIONS OF THE GENERALIZED LAPLACE'S EQUATION

1998 ◽  
Vol 13 (09) ◽  
pp. 715-725 ◽  
Author(s):  
S. CHATURVEDI
Keyword(s):  
Homogeneous Polynomial ◽  
Binomial Coefficients ◽  
Jack Polynomials ◽  
Laplace’S Equation ◽  
Linear Combinations ◽  
Laplace's Equation ◽  
Polynomial Solutions ◽  
Sutherland Model ◽  
Generalized Binomial Coefficients

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 up to k=6 are tabulated.

Sign in / Sign up

Export Citation Format

Share Document