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A Fuchsian matrix differential equation for Selberg correlation integrals
Fuchsian matrix differential equation Selberg correlation integrals
2010/11/12
We characterize averages of $\prod_{l=1}^N|x - t_l|^{\alpha - 1}$ with respect to the Selberg density, further contrained so that $t_l \in [0,x]$ $(l=1,...,q)$ and $t_l \in [x,1]$ $(l=q+1,...,N)$, in...
Difference system for Selberg correlation integrals
Difference system Selberg correlation integrals
2010/11/12
The Selberg correlation integrals are averages of the products $\prod_{s=1}^m\prod_{l=1}^n (x_s - z_l)^{\mu_s}$ with respect to the Selberg density. Our interest is in the case $m=1$, $\mu_1 = \mu$, w...