An Analytic Formula for the A_2 Jack Polynomials

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 $A_n$ Jack polynomials. This approach originated from the work [RIMS Kokyuroku 919 (1995), 27-34] 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.

Keywords

• Jack polynomials
• integral operators
• hypergeometric functions