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Re: Re: Different results with FourierTransform[]

• To: mathgroup at smc.vnet.net
• Subject: [mg97894] Re: [mg97882] Re: Different results with FourierTransform[]
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Wed, 25 Mar 2009 05:42:03 -0500 (EST)
• References: <gpl5sh$ou6$1@smc.vnet.net> <gpnscg$go5$1@smc.vnet.net> <200903241034.FAA19949@smc.vnet.net>

schochet123 at gmail.com wrote:
> [...]
> Unfortunately, there appears to be a bug in Mathematica's calculation
> of
> InverseFourierTransform of Tanh[x], as the original poster pointed
> out. The fact that the answer obtained is wrong can be seen from the
> fact that the answer is not odd, which contradicts the fact that the
> FourierTransform and InverseFourierTransform of odd functions are odd.
> 
> Sorry if some people see this message twice; when I originally posted
> it via thunderbird my message showed up in thunderbird on my local
> site but not in google groups.
> 
> Steve

Moderated group, takes maybe a day for messages to go out.

Devendra Kapadia located the bug in a special case handler (applicable 
when we have integral convergence at infinity, modulo a constant) and 
fixed it in the development Mathematica. Turns out to be a missplaced 
minus sign. From his note to me last week:

(ExpToTrig[-Exp[$FFC*I*s*t] should be ExpToTrig[Exp[-$FFC*I*s*t])

Was my bug from 4-5 years ago.

[Steve should not be surprised; he may recall me taking an occasional 
snooze in physics 112, where we covered Fourier transforms.]

Daniel Lichtblau
Wolfram Research

• References:
  • Re: Different results with FourierTransform[]
    • From: schochet123@gmail.com