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Re: Problem with an integral
*To*: mathgroup at smc.vnet.net
*Subject*: [mg95645] Re: [mg95571] Problem with an integral
*From*: "David Park" <djmpark at comcast.net>
*Date*: Fri, 23 Jan 2009 05:09:56 -0500 (EST)
*References*: <18607536.1232540493860.JavaMail.root@m02>
When I see an expression like:
fun = x^(n + 1)*E^(-x + (I*k)/x)
it always makes me cringe a little. That is because it has parameters and a
variable and it is always better to make these a part of the definition. So
I would write:
fun[n_, k_][x_] := x^(n + 1)*E^(-x + (I*k)/x)
Then if I wanted to see precisely what I was doing, I would use the
Student's Integral section of the Presentation package.
Needs["Presentations`Master`"]
integrate[fun[1, 1][x], {x, 0, \[Infinity]}]
% // UseIntegrate[]
% // N
giving...
\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Infinity]\)]\(\(
\*SuperscriptBox[\(E\), \(
\*FractionBox[\(I\), \(x\)] - x\)]\
\*SuperscriptBox[\(x\), \(2\)]\) \[DifferentialD]x\)\)
4 (MeijerG[{{}, {}}, {{0, 3/2, 2}, {1/2}}, 1/16] +
I MeijerG[{{}, {}}, {{1/2, 3/2, 2}, {0}}, 1/16])
1.67562 + 0.832688 I
If one wanted to do simplifications on the integrand or use other
integration techniques after the first step, that could also be done.
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/
From: Jepessen [mailto:jepessen at gmail.com]
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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