I have following summation that I want to implement inusing Mathematica,:
Sum[If[mSum[
If[m == 0 && n == 0
, Nothing
Nothing, (1/
z^2 + (1/(z - (m 2 \[Pi]π + n 2 \[Pi]π \[Tau]τ))^2 -
1/((m 2 \[Pi]π +
n 2 \[Pi]π \[Tau]τ))^2) /. {z -> \[Pi]π \[Tau]τ}) - (1/
z^2 + (1/(z - (m 2 \[Pi]π + n 2 \[Pi]π \[Tau]τ))^2 -
1/((m 2 \[Pi]π + n 2 \[Pi]π \[Tau]τ))^2) /. z -> \[Pi]π) //
Simplify]Simplify
], {m, -Infinity∞, Infinity∞}, {n, -Infinity∞, Infinity∞}
]
Above code returns a nicethe following result:
$-\frac{2 \left(\tau ^2-1\right)}{\pi ^2 \tau ^2}$
However, but if I remove the ifIf command in the above summation, Mathematica doesn't do the summation anymore, but I know the above expression is finite when m=0&&n=0 is finite. What's going on here?
