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MathGroup Archive 2005

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Re: Complex integration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55816] Re: Complex integration
  • From: dh <dh at metrohm.ch>
  • Date: Thu, 7 Apr 2005 05:09:55 -0400 (EDT)
  • References: <d305d3$rv7$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Berhard
considering your two integrands:
1) 2^(-(-12500 + w)^2/31250 - (-12500 + w + W)^2/
    31250)
and
2) 2^(-(-12500 + w)^2/31250 - (-12500 + w + W)^2/
     31250)*E^((-I)*Pi*Cos[(Pi*w)/64] +
    I*Pi*Cos[(Pi*(w + W))/64])

it is not surprising  that the second integral is much more difficult.

HOWEVER, if I try to do the second integral, Mathematica simply dies!!!
Here my versio of Mathematica:
$Version
"5.1 for Microsoft Windows (October 25, 2004)"

If somebody else could very this we will have a case for WRI

Sincerely, Daniel



Bernhard von Vacano wrote:
> Dear Group,
> 
> I am experiencing problems with a Mathematica simulation I am trying to 
> perform.
> 
> The first part of my notebook evaluates without any problems:
> 
> 
> ETL[w_] := Exp[-(w - w0)^2/width^2*2 Log[2]]
> 
> EPer[w_] := ETL[w]* Exp[I Pi Cos[2 Pi w/Wm]]
> EPerCC[w_] := ETL[w]* Exp[-I Pi Cos[2 Pi w/Wm]]
> 
> parameter := {w0 -> 12500, width -> 250, Wm -> 128}
> 
> AmpTL[W_] = Integrate[ETL[w]ETL[w + W] /. parameter, {w, 10000, 20000}]
> 
> 
> This is the first expression I need for plotting (in the Range of W = 
> 0..1000), and gives the correct results.
> With my so far limited mathematica skills, I could not get the following 
> modified expression to be evaluated:
> 
> AmpPer[W_] = Integrate[EPerCC[w]EPer[w + W] /. parameter, {w, 10000, 20000}]
> 
> Like this, it only produces "$RecursionLimit::reclim: "Recursion depth of 
> 256 exceeded." und "$IterationLimit::itlim: Iteration limit of 4096 
> exceeded."
> 
> I have tried other limits for the integration, indefinite integration and 
> NIntegrate, but so far it did not work. (At the moment, I am using 
> Mathematica 4).
> 
> Could anybody help me with this? I don't really know which parameters to use 
> or how to restate the problem to get it working. It doesn't seem too hard to 
> compute, does it?
> 
> 
> Thank you very much in advance,
> 
> Yours
> Bernhard 
> 
> 


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