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ExpIntegralEi


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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