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.. >