On Sep 14, 11:08 am, sps <[email protected]> wrote:
> How can I calculate this summation:
>
> summation(from:0,to:+oo,((2*I)^n/(n^3+1)*(1/4)^n))
>
> in sage?
>
First I tried this:
----------------------------------------------------------------------
| Sage Version 4.4.4, Release Date: 2010-06-23 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
Loading Sage library. Current Mercurial branch is: hackbranch
sage: var('n')
n
sage: sum(((2*I)^n/(n^3+1)*(1/4)^n),n,0,oo)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
TypeError: unable to make sense of Maxima expression '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)' in Sage
which made me want to know what Maxima was generating:
sage: maxima_console()
<snip>
(%i1) load(simplify_sum);
(%o1) /Users/.../sage-4.4.4/local/share/maxima/5.20.1/s\
hare/contrib/solve_rec/simplify_sum.mac
(%i2) simplify_sum(sum(((2*%i)^n/(n^3+1)*(1/4)^n),n,0,inf));
sqrt(3) %i + 1 sqrt(3) %i - 1
(%o2) %f ([1, 1, - --------------, --------------],
4, 3 2 2
sqrt(3) %i - 1 sqrt(3) %i
+ 1 %i
[2, - --------------,
--------------], --)
2
2 2
So looks like we need support for turning Maxima hypergeometric
functions into Sage ones! Burcin, does Pynac/Ginac support these?
> Can I find radius of convergence of series? How?
Can you give a more explicit example of what you'd like to calculate?
- kcrisman
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