Re: Problem with Integrate
- To: mathgroup at smc.vnet.net
- Subject: [mg9471] Re: [mg9423] Problem with Integrate
- From: "W. Meeussen" <w.meeussen.vdmcc at vandemoortele.be>
- Date: Thu, 6 Nov 1997 02:40:14 -0500
- Sender: owner-wri-mathgroup at wolfram.com
hi Pedro,
make a plot of the imaginary & real part of your function; then you will
see the divergence at x->1 and x->0.
So you could break up the integration in three parts:
In[106]:=
Integrate[Exp[-I w x] (1-Exp[I
w])/w,{x,-\[Infinity],0},Assumptions->{Im[w]== 0}]
Out[106]=
I - I Cos[w] + Sin[w]
---------------------
2
w
In[107]:=
Integrate[Exp[-I w x] (1-Exp[I w])/w,{x,0,1},Assumptions->{Im[w]==0}]
Out[107]=
2 2 -I (1 - 2 Cos[w] + Cos[w] + Sin[w]
) -------------------------------------
2
w
In[108]:=
Integrate[Exp[-I w x] (1-Exp[I
w])/w,{x,1,\[Infinity]},Assumptions->{Im[w]== 0}]
Out[108]=
2 2 I (-Cos[w] + Cos[w] + I
Sin[w] + Sin[w] ) ------------------------------------------
2
w
Add them, FullSimplify it, and you get 0, (zero, rien, ingenting, niks,
nada, zip).
So much for all your trouble, getting "nothing".
have fun too,
wouter.
At 01:56 5-11-97 -0500, Pedro A Santos wrote:
>Hello,
>
>I hope somebody can help me with a problem:
>
>When I try to use Integrate as
>
>In[1]= Integrate[Exp[-I*w*x]*(1-Exp[I*w])/w,{w,-Infinity, Infinity}]
>
>I get the answer
>
>\!\(\*
> RowBox[{
> \(Integrate::"idiv"\), \( : \ \),
> "\<"Integral of \!\(\(E\^\(\(-I\)\\ w\\ x\)\\ \((1 - E\^\(I\\
>w\))\)\)\/w\
>\) does not converge on \!\({\*InterpretationBox[\(-\\[Infinity]\), \
>DirectedInfinity[-1]], \*InterpretationBox[\"\\[Infinity]\", \
>DirectedInfinity[1]]}\)."\>"}]\)
>
>Even if I put the option PrincipalValue -> True. But if I write
>
>In[2]= InverseFourierTransform[(1-Exp[I*w])/w,w,x]
>
>I get the correct answer
>
>Out[2]= \!\(\(-I\)\ UnitStep[1 - x, ZeroValue \[Rule] 1\/2] +
> I\ UnitStep[\(-x\), ZeroValue \[Rule] 1\/2]\).
>
>Does somebody know why this happens? Thanks
>
>
>Pedro Santos
>
>
Dr. Wouter L. J. MEEUSSEN
w.meeussen.vdmcc at vandemoortele.be
eu000949 at pophost.eunet.be