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Different results with FourierTransform[]

• To: mathgroup at smc.vnet.net
• Subject: [mg97588] Different results with FourierTransform[]
• From: Wieland Brendel <wielandbrendel at gmx.net>
• Date: Mon, 16 Mar 2009 04:24:44 -0500 (EST)

Dear reader,
I somewhat stumbled over the following behaviour of mathematica: I tried 
to calculate the fouriertransform of Tanh[x]. I did this in two ways:

1. Directly:
InverseFourierTransform[Tanh[x], x, p]

2. Indirectly:
InverseFourierTransform[Tanh[B x], x, p]

where I set B -> 1 in the end.

However, the result between the two approaches differs: Whereas in the 
first approach I get a complex number (with both real and imaginary part 
being non-zero for almost all values of p), the result in the second 
approach yields NO real part; the imaginary part however is the same as 
in the first approach. Is there any explanation for this behaviour?

Thanks a lot in advance! I am really stuck with that...
Wieland

• Follow-Ups:
  • Re: Different results with FourierTransform[]
    • From: Richard Hofler <rhofler@bus.ucf.edu>