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SIGMA 3 (2007), 014, 11 pages math.CA/0701677
https://doi.org/10.3842/SIGMA.2007.014
Contribution to the Vadim Kuznetsov Memorial Issue
An Analytic Formula for the A2 Jack Polynomials
Vladimir V. Mangazeev
Department of Theoretical Physics, Research School of Physical Sciences and Engineering,
The Australian National University, Canberra, Australia
Received November 01, 2006, in final form January
05, 2007; Published online January 24, 2007
Abstract
In this letter I shall review my joint results with
Vadim Kuznetsov and Evgeny Sklyanin [Indag. Math. 14
(2003), 451-482] on separation of variables (SoV) for the An
Jack polynomials. This approach originated from the work [RIMS Kokyuroku
919 (1995), 27-34] where the integral
representations for the A2 Jack polynomials was derived. Using
special polynomial bases I shall obtain a more explicit expression
for the A2 Jack polynomials in terms of generalised
hypergeometric functions.
Key words:
Jack polynomials; integral operators; hypergeometric functions.
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