I'm wondering if there is any literature that deals with the integral of the following type
$$ \int \dfrac{1}{2\pi\sqrt{1-\rho^2}} \cdot \exp(-\dfrac{(a^2+b^2+2\rho ab)}{2(1-\rho^2)}) \cdot d\rho $$
which appears in Mehler's Formula for Hermite polynomials.
The expression to be integrated is the usual bi-variate Gaussian density, however I cannot find any reference when integrating with respect to $\rho$. I'd be very grateful if someone can point out any useful reference to look for. Thanks!