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Re: Problem with an integral

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  • Subject: [mg95617] Re: Problem with an integral
  • From: dh <dh at>
  • Date: Thu, 22 Jan 2009 07:14:39 -0500 (EST)
  • References: <gl72ql$cpm$>


Integrate gives a generic result, that is correct for almost all values, 

but does NOT take into account special behaviour for isolated values. 

E.g. set k=1 and look at the result from Assuming[{ n > 0}, 

Integrate[fun, {x, 0, \[Infinity]}]]. The result has the form of a 

difference of 2 summands that both have no numerical value for n==1. 

Therefore, this formula can  not be used for n==1. Due to numerical 

errors, it even fails for values of n close to 1. However, you may set 

k==1 and n==1, now Integrate gives the correct result.

hope this helps, Daniel

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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