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Hi, I have encountered an integral of the following type in an engineering application: $\int_{-\infty}^\infty dx \frac{1}{\sqrt{x^2+a^2}}\exp(-x^2/2+i x b)$, where $a$ and $b$ are real ($a$ could ...

The proof of the Wigner Semicircle Law comes from studying the GUE Kernel $$ K_N(\mu, \nu)=e^{-\frac{1}{2}(\mu^2+\nu^2)} \cdot \frac{1}{\sqrt{\pi}} \sum_{j=0}^{N-1}\frac{H_j(\lambda)H_j(\mu)}{2^j j!} ...