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Re: complex output for real integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg115867] Re: complex output for real integral
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Sun, 23 Jan 2011 05:36:37 -0500 (EST)

On 1/22/11 at 3:23 AM, tsariysk at craft-tech.com (Ted Sariyski) wrote:

>I get complex answer for an integral from Exp[1/x^3]/x^3 over the
>real axes:

>In[]:=f[n_] = Assuming[
>{Element[x, Reals], Element[n, Integers], n >= 1},
>Integrate[E^(1/x^3)/x^3, {x, n, Infinity}]
>]

>Out[]:= 1/6 (-1)^(1/3) (-3 Gamma[5/3] + 2 Gamma[2/3, -(1/n^3)])

>The imaginary part of f[n] is everywhere   ~10^-16  and I could
>ignore it but I guess there is a better approach.

You could use Chop, i.e.

In[7]:= ans = 1/6 (-1)^(1/3) (-3 Gamma[5/3] + 2 Gamma[2/3, -(1/n^3)]);

In[8]:= Chop[ans /. n -> 1 // N]

Out[8]= 0.781197

But this is essentially the same as ignoring it.

Note, the reason you are seeing this is due to the limitations
of machine precision arithmetic. That is:

In[9]:= Im[N[ans /. n -> 1, 50]]

Out[9]= 0``50.25775441372254

Demonstrating the true value of the imaginary part is zero.



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