FourierTransform gives strange result
- To: mathgroup at smc.vnet.net
- Subject: [mg9731] FourierTransform gives strange result
- From: Pedro A Santos <pasantos at math.ist.utl.pt>
- Date: Tue, 25 Nov 1997 00:06:31 -0500
- Organization: I.S.T. - Portugal
- Sender: owner-wri-mathgroup at wolfram.com
Hello,
Trying the following in Mathematica 3.0 gives
In[1]:=<<Calculus`FourierTransform`
$FourierOverallConstant = 1
$FourierFrequencyConstant =-2*Pi
In[2]:=FourierTransform[UnitStep[x]*Exp[I*k0*x*Cos[\[Theta]]],x,y,
Assumptions->{Im[k0]>0,Re[k0] > 0}]
Out[2]:=-(I/(2*Pi*y - k0*Cos[\[Theta]])) +
1/2*DiracDelta[y - (k0*Cos[\[Theta]])/(2*Pi)]
and the DirecDelta part seems not to be correct. If one specifies k0:
In[3]:= k0=10^6+10^(-6)*I
and repeat the FourierTransform, then Mathematica returns the correct
result(without the DiracDelta). Does anyone know why this strange
result appears?
Thanks
Pedro Santos