This question is related to another answered before
distribution on the inverse Wishart matrix eigenvalues summation
my question is, is their finite expression for the expectation of
\begin{align}
{\rm E}[{e^{ - \frac{b}{{1 + ax}}}}]
\end{align}
where $x$ is
Marchenko-Pastur distribution variable.
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$\begingroup$ just integrate $\int dx e^{-b/(1+ax)}\rho(x)dx$ with $\rho(x)$ the MP distribution; this integral cannot be evaluated in closed form, but you can evaluate it numerically. $\endgroup$– Carlo BeenakkerCommented May 16, 2020 at 9:22
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$\begingroup$ @Carlo Beenakker Sir is there closed for the Laplace transform of MP distribution $\endgroup$– hichem hbCommented May 17, 2020 at 3:33
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$\begingroup$ no there is not. $\endgroup$– Carlo BeenakkerCommented May 17, 2020 at 7:26
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