On Sat, Aug 30, 2008 at 4:34 PM, Ondrej Certik <[EMAIL PROTECTED]> wrote:
> On Sat, Aug 30, 2008 at 6:06 AM, tkeller <[EMAIL PROTECTED]> wrote:
>>
>> I asked this question myself a few months ago, and the easiest 2
>> solutions seem to be utilizing sympy or maxima.
>>
>> Via sympy it is:
>> import sympy
>> sympy.var('x')
>> print sympy.sum(2**(-x), (x, 1, oo))
>>
>> I'm taking this from a question I posed on the sympy message list:
>> http://groups.google.com/group/sympy/browse_frm/thread/5348ded3ebe8a25e?tvc=1
>>
>> It should return a result of 1, but in sage 3.1.1 it returns 1-2*2**(1-
>> Infinity). While technically correct, this should clearly return 1
>> when simplified so I guess there is some complication when
>> transferring between modules. Ondrej will assuredly give more useful
>> information if he sees this.
>
> sympy returns 1 for me:
>
> In [1]: sum(2**(-x), (x, 1, oo))
> Out[1]: 1
>
>
>>
>> More specifically , your example using m=2 is:
>> sympy.sum(1/((x+2)**3)),(x,1,oo))
>>
>> Unfortunately this returns
>> Sum((2 + x)**(-3), (x, 1, Infinity))
>
> In [4]: sum(1/(x+2)**3,(x,1,oo))
> Out[4]: Sum((2 + x)**(-3), (x, 1, oo))
>
> Thanks for the spot, I reported it:
>
> http://code.google.com/p/sympy/issues/detail?id=1066
>
>>
>> n() on this function does not work, maybe a sympy equivalent would?
>> It may work better with a %python header, though I haven't tested this
>> yet (if you use the notebook).
>
> It does work in sympy:
>
> In [5]: N(sum(1/(x+2)**3,(x,1,oo)))
> Out[5]: 0.0770569031595943
Here is how you can get the result using sympy's nsimplify, if you
know the result should contain zeta(3):
In [35]: e = sum(1/(x+2)**3,(x,1,oo))
In [36]: nsimplify(e, [zeta(3)])
Out[36]: -9/8 + ΞΆ(3)
nsimplify takes the floating point approximation of the result (by
default currently at least 30 digits) and tries to get the same
results using a simple formula.
See nsimiplify??. You need the latest hg version of sympy, this is
quite recent code.
Ondrej
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