Does anyone know how to get an analytic expression of this?
$$\int^L_{-L} dx \frac{e^{- m\sqrt{x^2+b^2}}}{\sqrt{x^2 + b^2}}e^{ikx} $$ where $k = \dfrac{n\pi}{L}$, $m$, and $b$ are real parameters.
or $$\int^L_{-L} dx \frac{e^{- m|x|}}{\sqrt{x^2 + b^2}} e^{ikx}= \int^L_{0} dx \frac{2\cos{(kx)}e^{- mx}}{\sqrt{x^2 + b^2}}$$ ??
This is a Fourier transform of quasi-one-dimensional Yukawa potential, where b is the fixed width and x is the length between two sources. I feel like this could be related with modified Bessel function of second kind with complex arguments but I am not certain about it.