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RE: ExpIntegralEi

• To: mathgroup at smc.vnet.net
• Subject: [mg18491] RE: [mg18463] ExpIntegralEi
• From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
• Date: Wed, 7 Jul 1999 23:08:47 -0400
• Sender: owner-wri-mathgroup at wolfram.com

Lionel ARNAUD reported the following with version 3.0.
-------------------------

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 !
----------------------
Lionel,

Version 4.0 gives the same result.  I wonder if the difference has to due
with branch cuts along the path of integration. It may be that the two
commands are integrating along different paths in the complex plane.

I think Exp[z] has a branch cut where Im[z]=(Pi+2*n*Pi) (n is an integer).
However it looks like the integration path doesn't cross a branch cut, so I
am puzzled.

Regards,
Ted Ersek