An Analytic Formula for the A_2 Jack Polynomials

Details An Analytic Formula for the A_2 Jack Polynomials An Analytic Formula for the A_2 Jack Polynomials

2007-01-24

arxiv.org/abs/math/0701677v1

SIGMA 3 (2007), 014, 11 pages

Mathematics

Classical Analysis and ODEs

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym

Scientific paper

10.3842/SIGMA.2007.014

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.

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