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I am trying to determine the fourier transform of the hyperbolic tangent function. I don't have a lot of experience with Fourier transforms and after searching for a bit I've come up empty handed on this specific issue.

So what I want to calculate is:

##\int\limits_{-\infty}^\infty e^{-it\omega}\text{tanh}(bt) dt##

where ##b## is some constant.

Using ##\text{tanh}(bt)=\frac{e^{bt}-e^{-bt}}{e^{bt}+e^{-bt}}## leads to a mess of exponential functions, and does not bring me closer to a solution. Perhaps there is some other way, using tricks specific to calculating Fourier transforms that could be helpful here?

Any suggestions are most appreciated

J

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# A Fourier transform of hyperbolic tangent

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