Sage incorrectly evaluates series
It incorrectly evaluates $\displaystyle\sum_{n=0}^{\infty}\frac{1}{((2n+1)^2-4)^2}=\frac{\pi^2}{64}-\frac{1}{12}$, but correct answer is $\displaystyle\frac{\pi^2}{64}$
It incorrectly evaluates $\displaystyle\sum_{n=0}^{\infty}\frac{1}{((2n+1)^2-4)^2}=\frac{\pi^2}{64}-\frac{1}{12}$, but correct answer is $\displaystyle\frac{\pi^2}{64}$
Indeed:
sage: n = var('n')
sage: sum(1/((2*n+1)^2-4)^2, n, 0, Infinity)
1/64*pi^2 - 1/12
See ticket #22005. Mathematica does it correctly:
sage: sum(1/((2*n+1)^2-4)^2, n, 0, Infinity, algorithm='mathematica')
1/64*pi^2
Giac gives this:
sage: sum(1/((2*n+1)^2-4)^2, n, 0, Infinity, algorithm='giac')
1/32*Psi(-1/2, 1) - 1/8
And SymPy seems to do it correctly:
sage: from sympy.abc import n
sage: from sympy import summation, oo
sage: A = summation(1/((2*n+1)^2-4)^2, (n, 0, oo))
sage: A._sage_()
1/64*pi^2
I created ticket #22004 so that one can do:
sage: sum(1/((2*n+1)^2-4)^2, n, 0, Infinity, algorithm='sympy')
1/64*pi^2
This may actually be https://sourceforge.net/p/maxima/bugs... which is apparently fixed in upstream.
Asked: 2016-12-01 02:50:57 -0600
Seen: 131 times
Last updated: Dec 01 '16
Unexpected result for the sum of a series
Convert exponential form to hyperbolic functions
integrate sqrt(1-cos(x)), integr.interval from 0 to 2*pi
Making a dictionary of matrices, and save the session
Detecting series divergence automatically
def f(x): evaluvates individually but not inside plot
Thanks for reporting !