# Question:How can I get Maple to find the Fourier transform of a logistic pdf? Also, a question about subs() vs. algsubs().

## Question:How can I get Maple to find the Fourier transform of a logistic pdf? Also, a question about subs() vs. algsubs().

Maple 2019

I'm a Maple novice.  I have two questions.  (1) I'm trying to use Maple to confirm some Fourier transforms of selected probability density functions.  In general I've succeeded, but Maple fails to find the Fourier transform of the pdf of a logistic random variable with mean 0.  Please explain how I can get Maple to carry out this request.  I've attached a Maple file with my work to this question.  (2) At several points in my computations, I wish to substitute 2*Pi*xi for omega.  I have an expression containing two omegas.  If I use algsubs(), only one of the two omegas is replaced.  I have to use subs() to replace both omegas.  Why is this?

Use Maple to confirm selected Fourier transform of logistic random variable

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Wikipedia's article on "Logistic distribution" gives a characteristic function that implies that the Fourier transform of this pdf should equal Pi*a*omega/sinh(Pi*a*omega).

Unit rectangular function

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