       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
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]
>
> 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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