Does anyone know how to integrate this function?
$$\int_{-\infty}^\infty e^{- a i t+ b \sqrt{c+t^2}}dt$$
I am thinking of using transformation like $\log{\mu}=\sqrt{1+t^2}$, but it is taking me nowhere. Does anyone have a better suggestion to do this integral? $a$, $b$, and $c$ are real constants; $i$ is the imaginary unit.