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Function expansion in high partition Jack polynomials?

For Jack polynomials $J_\lambda^\alpha(x_1,x_2,...,x_n)$ there exists i.e. the following relation $$\sum_\lambda J_\lambda^\alpha(x_1,x_2,...,x_n)J_{\lambda'}^{\frac{1}{\alpha}}(y_1,y_2,...,y_m)=\...
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