- [math]\displaystyle{ \displaystyle \sum_{n=-\infty}^{\infty} f(n)=-\sum (\text{residue of $\pi \cot(\pi z)f(z)$ at each pole of $f$}) }[/math]
- [math]\displaystyle{ \displaystyle \sum_{n=-\infty}^{\infty} (-1)^n f(n)=-\sum (\text{residue of $\pi \csc(\pi z)f(z)$ at each pole of $f$}) }[/math]