       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>

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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?

>