Re: FoourierTransform of a function defined in sections

• To: mathgroup at smc.vnet.net
• Subject: [mg70190] Re: FoourierTransform of a function defined in sections
• From: Roland Franzius <roland.franzius at uos.de>
• Date: Sat, 7 Oct 2006 07:07:02 -0400 (EDT)
• Organization: Universitaet Hannover
• References: <eg4soa\$ffu\$1@smc.vnet.net>

Eckhard Schlemm schrieb:
> Hello,
>
> I want Mathematica to calculate the FourierTransform of a function which is
> defined by Sin[x]^2 for Abs[x]<PI and zero else. I tried and defined the
> function g as follows:
>
> g[x_]:=If[Abs[x]>PI,0,Sin[x]^2];
>

Should be Pi instead of PI I assume

> That works fine. But if I have mathematica try to determine the
> FourierTransform by
>
> FourierTransform[g[x],x,p]
>
> I always get the error that the recursion limit and the iteration limit were
> exceeded...
>
> what am I'm doing wrong?

No idea. Recursion error may indicate that g or x or p have values already?

g[x_] := UnitStep[Pi - x]UnitStep[Pi + x] Sin[x]^2

FourierTransform[g[x], x, k]

-((2*Sqrt[2/Pi]*Sin[k*Pi])/(-4*k + k^3))

h[x_] := If[-Pi < x < Pi, Sin[x]^2, 0]

FourierTransform[h[x], x, k]

-((2*Sqrt[2/Pi]*Sin[k*Pi])/(-4*k + k^3))

--

Roland Franzius

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