An Analytic Formula for the A 2 Jack Polynomials
Copyright policy )An Analytic Formula for the A 2 Jack Polynomials
In this letter I shall review my joint results with Vadim Kuznetsov and Evgeny Sklyanin [Indag. Math. 14 (2003), 451-482, math.CA/0306242] on separation of variables for the $A_n$ Jack polynomials. This approach originated from the work [RIMS Kokyuroku 919 (1995), 27-34, solv-int/9508002] where the integral representations for the $A_2$ Jack polynomials was derived. Using special polynomial bases I shall obtain a more explicit expression for the $A_2$ Jack polynomials in terms of generalised hypergeometric functions.
This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
- Australian National University Australia
Symmetric functions and generalizations, Nonlinear Sciences - Exactly Solvable and Integrable Systems, integral operators, FOS: Physical sciences, Groups and algebras in quantum theory and relations with integrable systems, Mathematical Physics (math-ph), Orthogonal polynomials and functions associated with root systems, Other hypergeometric functions and integrals in several variables, Mathematics - Classical Analysis and ODEs, QA1-939, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Jack polynomials, Exactly Solvable and Integrable Systems (nlin.SI), Exactly solvable models; Bethe ansatz, Mathematics, Mathematical Physics, hypergeometric functions
Symmetric functions and generalizations, Nonlinear Sciences - Exactly Solvable and Integrable Systems, integral operators, FOS: Physical sciences, Groups and algebras in quantum theory and relations with integrable systems, Mathematical Physics (math-ph), Orthogonal polynomials and functions associated with root systems, Other hypergeometric functions and integrals in several variables, Mathematics - Classical Analysis and ODEs, QA1-939, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Jack polynomials, Exactly Solvable and Integrable Systems (nlin.SI), Exactly solvable models; Bethe ansatz, Mathematics, Mathematical Physics, hypergeometric functions
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