Re: [Maxima-discuss] simplify_sum leads to a wrong value

[philippe <rou...@gm...>]

Hi,

I've check the results with SAgeMath (which obviously call maxima for
this computation) and wolframalpha. This last one found another closed
form for the series :

https://photos.app.goo.gl/XGoyMm9TCa6t34gs7

and find the same numerical value  2.564... for the maxima formula with erf:

https://photos.app.goo.gl/kWuP9xnw739keRjx8

So the simplify_sum has a bug (not float)

Philippe

Le 07/04/2020 à 22:52, philippe a écrit :
> Hi,
> 
> I want to check the limit of the following serie
> 
> sum((k*sin((k*%pi)/3))/(4*k^2-1),k,1,inf)
> 
> I know it converge to (sqrt(3)*%pi)/16=0.3400873807939158...
> 
> simplify_sum find the limit in terms of erf(%i) but floating point
> approximation is far from the expected value : 2.564242426927912...
> 
> I don't know if the problem comes from simplify_sum or floating point
> approximations of erf function, but there is no error for the similar serie
> 
> sum(k*sin(k*%pi/2)/(4*k^2-1),k,1,inf)=sqrt(2)*%pi/16
> 
> if some one is interested in this problem here is a short piece of code
> to test it :
> 
> load(simplify_sum)$
> S2:sum(k*sin(k*%pi/3)/(4*k^2-1),k,1,inf)$
> S2s:simplify_sum(S2)$
> S2c:sqrt(3)*%pi/16$
> print(S2,"=",S2s,"=",float(S2s));
> print(S2,"=",S2c,"=",float(S2c));
> 
> thanks for reading,
> Philippe
>