This is a known bug, https://github.com/sympy/sympy/issues/8404

A._sage_() works because exp_polar(I*pi) is -1 in sage and is unevaluated
in SymPy.


Isuru Fernando

On Fri, Dec 2, 2016 at 2:55 PM, Sébastien Labbé <sla...@gmail.com> wrote:

> Can SymPy tell me that A = 1/64*pi**2 by simplifying the polylog in below
> example?
>
> >>> from sympy.abc import n
> >>> from sympy import summation, oo
> >>> A = summation(1/((2*n+1)^2-4)^2, (n, 0, oo))
> >>> A
> -polylog(2, exp_polar(I*pi))/16 + pi**2/96
> >>> A.simplify()
> -polylog(2, exp_polar(I*pi))/16 + pi**2/96
>
> because it seems doable:
>
> 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
>
> This came up in https://ask.sagemath.org/question/35839/sage-
> incorrectly-evaluates-series/
>
> Sébastien
>
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