[Maxima] Integrate Dirichlet distribution

[Barton Willis]

-----maxima-bounces at math.utexas.edu wrote: -----

>> Using hyperint, Maxima can integrate over x_1 (or x_2), but it cannot 
>> handle the iterated integral.
>
>Just to make completely clear: You're saying Maxima can't do the 
>iterated integral *and* there's no easy way to extend it to do so?
>
>John.

I don't know exactly what "easy" means in this context, but I think
your statement is more true than false. I don't know of a general workaround
or optional package that can handle the iterated integral.

When 1-c is explicitly a negative integer, Maxima can handle the iterated integral

 (%i34) -(hypergeometric([a,1-c],[a+1],-1/(x_2-1))*x_2^(b-1)*%e^(c*log(-x_2)))/((x_2/(x_2-1))^c*(a*x_2-a))$
 (%i35) factor(integrate(subst(c=3,%),x_2,0,1));

 "Is  "b"  positive, negative, or zero?"pos;
 (%o35) (a^2*b^2+a*b^2+a^2*b-a*b+4)/(a*(a+1)*(a+2)*b*(b+1)*(b+2))


--Barton