[Python] Why can't SymPy calculate the Sum(1 / ((k + 1) ** 4 + 1), (k,-oo,oo)) when it appears...

I'm using Sympy for some numeric calculations, specifically for infinite summations. The following code returns 0:

import sympy as sp
from sympy.abc import k

sp.summation(1 / ((k + 1) ** 4 + 1), (k, -sp.oo, sp.oo))


However, all elements of this sum are positive. The docs say that if the sum is incalculable, it will be returned as-is, however that's not the case here. Makes me wonder if there are other cases when SymPy is wrong.

In which cases does SymPy not guarantee correctness of calculations?

Edit: This sum is calculable (can be calculated without special functions e.g. via the residual theorem, any modern LLM can guide you through the process); it converges to a positive number. Most likely, SymPy would not be able to handle it, but I expect it to at least admit that it cannot instead of returning a false answer.

Continue reading...