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Student Support Forum: 'Inverse Fourier Transform of Hankel function ?' topicStudent Support Forum > General > "Inverse Fourier Transform of Hankel function ?"

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Lucas
03/13/13 6:07pm

Hello,

It's been a while since I last used mathematica, so my apologies if the answer turns out to be obvious.

I've solved the radially symmetric Helmholtz equation in 2D-coordinates (waves from point source in 2D). The solution u is a function of the distance 'r' from the source and the wave number 'k'. Since the wavespeed is known this can also be written in terms of the distance 'r' and angular frequency 'omega'.

u(r,omega) contains the term HankelH2(r*omega/c) in which c is the wavespeed and r is the 'radius' with r > 0.

The question is: How can I inverse Fourier transform the Hankel of zeroth order and second kind?

I have tried:
S[om_] := HankelH2[0, om]
s[t_] := InverseFourierTransform[S[om], om, t,
FourierParameters -> {1, -1}]

But this doesn't seem to work. Mathematica just keeps on churning. I guess this means that there is no analytic solution? Is there some way in which I can make Mathematica evaluate it ? Or should I resort to a discretized version and IFFT it?





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