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Fourier-cosine transform of hyperbolic function

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Could you help me please with the Fourier cosine transform with respect to x variable of the following function?
tanh[b(a^2+x^2)^1/2]cos(ax)/((a^2+x^2)^1/2)
Recall, that the Fourier cosine transform of the function f(x) defines by
int(f(x),0,infinity)
  1 Comment
Kevin Claytor
Kevin Claytor on 19 Jul 2012
Could you be more specific, what do you need help with?

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Accepted Answer

Walter Roberson
Walter Roberson on 19 Jul 2012
If there is any solution at all, it would have to involve a transformation of variables. I tried a number of different representations of tanh() but none of them had an analytical solution for the fourier cosine transform.
Note: please edit existing questions instead of deleting them and re-posting.
  4 Comments
Walter Roberson
Walter Roberson on 20 Jul 2012
I would not expect so, but I cannot rule it out. There are some known cases where the MATLAB Symbolic Toolbox can integrate some things that Maple cannot, but I have only seen one such case myself, and I have seen a number of integrals that Maple can handle easily that the Symbolic Toolbox cannot.
If you do not already have the Symbolic Toolbox you could request a trial of it to test with.

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