[Maxima-discuss] simplify_sum leads to a wrong value

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

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