Re: Multiple choice question

*To*: mathgroup at smc.vnet.net*Subject*: [mg26743] Re: Multiple choice question*From*: "A. Ciarkowski" <aciark at ippt.gov.pl>*Date*: Fri, 19 Jan 2001 02:14:18 -0500 (EST)*Organization*: http://news.icm.edu.pl/*References*: <943dj3$cjh@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Since the integral in question can alternatively be calculated as: In[1]:= Limit[-Exp[-z] ExpIntegralEi[z] /. z->(e-I 2)(1+I), e->0] // N Out[1]:= -0.547745-0.532287 I , Out[13] (lucky 13!) seems to be valid. Adam F.H.Simons at tue.nl wrote: > > We compute an integral in four different ways (one numerically and three > symbolically). Which of the following results is correct? > > In[12]:= > NIntegrate[ Exp[I t 2 ]/(t-1-I), {t, 0, Infinity}, Method->Oscillatory] > > Out[12]= > -0.934349-0.70922 I > > In[13]:= > Integrate[ Exp[I t 2 ]/(t-1-I), {t, 0, Infinity}] // N > > Out[13]= > -0.547745-0.532287 I > > In[14]:= > N[Integrate[ Exp[I t u ]/(t-1-I), {t, 0, Infinity}] /. u-> 2] > > Out[14]= > -0.16114-0.355355 I > > In[15]:= > N[ Integrate[#, {t, 0, Infinity}]& /@ ComplexExpand[ Exp[I t 2 ]/(t-1-I), > TargetFunctions->{Re, Im}] // Expand ] > > Out[15]= > -0.724677-0.145683 I > > (And why are the other results false?) > > Fred Simons > Eindhoven University of Technology