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A motivating example: Consider the Hypergeometric equation $$z(1-z) \frac{d^2y}{dz^2}+(c-(a+b+1)z) \frac{dy}{dz}-aby=0,$$ it has a solution given by the Gauss's Hypergeometric function $$_2F_1(a,b;c;z)...

Let $ \mu $ be the Gaussian measure $ d\mu(x) = e^{-x^2/2} \frac{dx}{\sqrt{2\pi} } $. I am interested in the following random matrix integral defined for all $ s \in \mathbb{R} $, $ N \geq 1 $ and $ a ...