On Homogeneous Polynomial Solutions of the Moisil-Théodoresco System in ℝ3

2008 ◽  
Vol 9 (1) ◽  
pp. 199-212 ◽  
Author(s):  
Richard Delanghe
Keyword(s):  
Homogeneous Polynomial ◽  
Polynomial Solutions

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.

scholarly journals ON PROPERTIES OF FINITE-ORDER MEROMORPHIC SOLUTIONS OF A CERTAIN DIFFERENCE PAINLEVÉ I EQUATION

2011 ◽  
Vol 85 (3) ◽  
pp. 463-475 ◽  
Author(s):  
MEI-RU CHEN ◽  
ZONG-XUAN CHEN
Keyword(s):  
Finite Order ◽  
Meromorphic Solutions ◽  
Rational Solutions ◽  
Polynomial Solutions ◽  
The Difference ◽  
Image Position

AbstractIn this paper, we investigate properties of finite-order transcendental meromorphic solutions, rational solutions and polynomial solutions of the difference Painlevé I equation where a, b and c are constants, ∣a∣+∣b∣≠0.

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