On 2012-05-15, kcrisman <kcris...@gmail.com> wrote:

> (%i3) domain:complex;
>
> (%o3) complex
> (%i4) integrate(x*cos(x^3),x,0,1/2);
>
> (%o4) 
> gamma_incomplete(2/3,%i/8)/6+gamma_incomplete(2/3,-%i/8)/6-gamma(2/3)/3

Hmm. I get a different result. I am using the current Git version.

domain : complex;
integrate (x*cos(x^3), x, 0, 1/2);
 =>
%i*gamma_incomplete(2/3,%i/8)/(4*sqrt(3))
 -gamma_incomplete(2/3,%i/8)/12-%i*gamma_incomplete(2/3,-%i/8)/(4*sqrt(3))
 -gamma_incomplete(2/3,-%i/8)/12+gamma(2/3)/6
expand (float (%));
 => .1247560409610377

That's gratifying, but the problem, as I'm sure you know, is that the
user won't know they have to change a global variable.

> I don't see any of those up here, though, and the gamma_incomplete 
> evaluation is correct (gives the same via W|A, Sage = Pari in my version, 
> mpmath, and Maxima).  I think that Maxima is somehow using the "real" 
> antiderivative, if that makes sense - is that possible, Robert?

It seems plausible, but I don't know the integration code very well.

best

Robert Dodier


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