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Is there any way to solve this integral?

$\int_{-\infty}^{\infty}\frac{e^{qiy -K(\sqrt{\lambda -a-iy}-\sqrt{\lambda})}}{a+iy} dy$ where $K,\lambda, a$ and $q$ are real numbers and $K>0$, $a>0$, $\lambda > 0$ and $q<0$

I have tried the standard contour approaches, but the branch cut makes it complicated on the lower half plane, and the integrand grows unbounded on the upper half plane.

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    Let the quantity underneath the radical sign equal $x^2$. Then your integral becomes$a$combination between the [Gaussian](http://en.wikipedia.org/wiki/Gaussian_integral) and [exponential integral](http://en.wikipedia.org/wiki/Exponential_integral).2013-12-11

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