Re: complex output for real integral
- To: mathgroup at smc.vnet.net
- Subject: [mg115872] Re: complex output for real integral
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Sun, 23 Jan 2011 05:37:38 -0500 (EST)
f[n_Integer?Positive] = Assuming[
{Element[x, Reals], Element[n, Integers], n >= 1},
Integrate[E^(1/x^3)/x^3, {x, n, Infinity}]]
1/6 (-1)^(1/3) (-3 Gamma[5/3] + 2 Gamma[2/3, -(1/n^3)])
The imaginary part is less than 10^-100 for n <= 100
Union[Chop[Im /@ N[f /@ Range[100], 100], 10^-100]]
{0}
Bob Hanlon
---- Ted Sariyski <tsariysk at craft-tech.com> wrote:
=============
Hi,
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.
I'll appreciate any help.
--Ted