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Re: Problem with an integral
*To*: mathgroup at smc.vnet.net
*Subject*: [mg95617] Re: Problem with an integral
*From*: dh <dh at metrohm.com>
*Date*: Thu, 22 Jan 2009 07:14:39 -0500 (EST)
*References*: <gl72ql$cpm$1@smc.vnet.net>
Hi,
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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