On Sep 17, 3:17 pm, sps <[email protected]> wrote:
> Can you explicitly write the results?
This might help you:
(%i2) display2d:false;
(%o2) false
(%i3) load(simplify_sum);
(%o3) "/Users/.../sage-4.4.4/local/share/maxima/5.20.1/share/contrib/
solve_rec/simplify_sum.mac"
(%i4) simplify_sum(sum(((2*%i)^n/(n^3+1)*(1/4)^n),n,0,inf))
;
(%o4) %f[4,3]([1,1,-(sqrt(3)*%i+1)/2,(sqrt(3)*%i-1)/2],
[2,-(sqrt(3)*%i-1)/2,(sqrt(3)*%i+1)/2],%i/2)
So this is the hypergeometric function F_{4,3} (where usually the 4 is
on the left and the three on the right) evaluated at the values 1, 1,
and so one, where %i is just one of the square roots of negative one.
You'll note that there are two sets of things to evaluate it at, plus
the third (i/2). These are not necessarily easy to compute.
See http://mathworld.wolfram.com/GeneralizedHypergeometricFunction.html,
for instance. I don't know that I can make this any easier to
compute, though! But unfortunately I cannot make the hypergeometric
functions easy (though they are very useful).
I'm not quite sure if this is the answer you are looking for or not,
so let us know.
- kcrisman
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