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Computing Fourier transforms and equivalent integrals

Posted 27 days ago

Wolfram Alpha seems to handle the following:
FFT 1/x^2 exp(–x^2)
But not the equivalent integral (recognized input, no output):
int exp(–x^2)/x^2 exp(ixt), x=-inf, inf

Is there a syntax problem here, do I need to upgrade to Pro, Pro Plus? Ultimately I'd like to find more complicated FTs, such as:
FFT 1/x^2 exp(–x^p)
int exp(–x^2)/x^p exp(ixt), x=-inf, inf
(p > 3/2)
(WA cannot handle either of these!)

POSTED BY: S. Lake
4 Replies

POSTED BY: Mariusz Iwaniuk

Those integrals do not converge due to the singularity at the origin. You might try adding GenerateConditions->False to Integrate[…] to see if that helps.

POSTED BY: Daniel Lichtblau
Posted 26 days ago

Many Thanks, this worked on Wolfram Cloud, as you suggested:

FourierTransform[(1/x^p)*Exp[-x^2],x,w,Assumptions -> p > 3/2]
POSTED BY: S. Lake

With Mathematica:

Regards M.I.

POSTED BY: Mariusz Iwaniuk
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