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Re: Problem with an integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg95618] Re: Problem with an integral
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Thu, 22 Jan 2009 07:14:50 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <gl72ql$cpm$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

Mathematica can't find a closed form for unknown n
and

integral[nn_]:=
  FullSimplify[
   Assuming[{k > 0 && Element[k, Integers]},
    Integrate[Evaluate[fun/. n->nn], {x, 0, \[Infinity]}]]]

give you analytic, and finite results for the corresponding n

Regards
   Jens

Jepessen wrote:
> Hi.
> 
> I'm working with a little problem in Mathematica 7.0.0.
> I want to integrate this function
> 
> fun = x^(n + 1)*E^(-x + (I*k)/x)
> 
> Assuming that both n and k are greater than zero, I write
> 
> integral = FullSimplify[Assuming[{k > 0, n > 0}, Integrate[fun, {x, 0,
> \[Infinity]}]]]
> 
> And I obtain a symbolic result.
> But, when I want to put some specific value, like this
> 
> integral /. {n -> 1, k -> 1}
> 
> I obtain always ComplexInfinity, and/or other errors.
> So, I've tried to evaluate numerically the integral for the same
> specific values, in this way
> 
> NIntegrate[Evaluate[fun /. {n -> 1, k -> 1}], {x, 0, \[Infinity]}]
> 
> And I obtain a finite numeric result. So, there's some error in
> symbolic computation, or I miss something when I try to integrate the
> formula?
> 
> Thanks for answers
> 


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