Re: ExpIntegralEi

• To: mathgroup at smc.vnet.net
• Subject: [mg18479] Re: ExpIntegralEi
• From: "Kevin J. McCann" <kevinmccann at Home.com>
• Date: Wed, 7 Jul 1999 23:08:41 -0400
• Organization: @Home Network
• References: <7lunja\$lh6@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```A plot of the Re and Im parts indicates that the analytic integration is
wrong, since the Im part is never larger than about 0.1 over the square
region.  I would bet on NIntegrate here.

Kevin

Lionel ARNAUD <arnaud at lmt.ens-cachan.fr> wrote in message
news:7lunja\$lh6 at smc.vnet.net...
> Hello,
>
> I am from LMT-Cachan FRANCE, working with MATHEMATICA V.3, I made this
> calculation:
>
> c2 = -0.05018627683354541 - 0.153047656745338 I;
> c3 = -0.7828709924214918 + 0.2780791279205129 I;
> c5 = -0.6758555487562639 - 0.04753624179417532 I;
>
> Integrate[Exp[beta*c2+s*(c3+beta*c5)], {s,0,1},{beta,0,1}]
>
> NIntegrate[Exp[beta*c2+s*(c3+beta*c5)], {s,0,1},{beta,0,1}]
>
> The results given are:
> -0.228103 + 10.5644 I
>  0.587252 +  0.0191685 I
>
> Not the same !
>
> Options of accuracy, algorithm,... don't change much the result, even if
> you change c2, c3 or c5 a little. In fact the Exp[beta...] is very regular
> and you can plot it and observe that the good result is given by the
Nintegral.
> It seems that the formal integration given by Mathematica
> is not totally correct.
>
> If you can tell me more, I am interested..
>

```

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