       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:=
Limit[-Exp[-z] ExpIntegralEi[z] /. z->(e-I 2)(1+I), e->0] // N

Out:= -0.547745-0.532287 I  ,

Out (lucky 13!) seems to be valid.

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:=
> NIntegrate[  Exp[I t  2 ]/(t-1-I), {t, 0, Infinity}, Method->Oscillatory]
>
> Out=
> -0.934349-0.70922 I
>
> In:=
> Integrate[  Exp[I t  2 ]/(t-1-I), {t, 0, Infinity}]  // N
>
> Out=
> -0.547745-0.532287 I
>
> In:=
>  N[Integrate[  Exp[I t  u ]/(t-1-I), {t, 0, Infinity}] /. u-> 2]
>
> Out=
> -0.16114-0.355355 I
>
> In:=
> N[ Integrate[#, {t, 0, Infinity}]& /@ ComplexExpand[ Exp[I t  2 ]/(t-1-I),
> TargetFunctions->{Re, Im}] // Expand ]
>
> Out=
> -0.724677-0.145683 I
>
> (And why are the other results false?)
>
> Fred Simons
> Eindhoven University of Technology

```

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