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

```

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