Abel-Plana formula

Etymology
Discovered independently by Niels Henrik Abel (1823) and Giovanni Antonio Amedeo Plana (1820).

Proper noun

 * 1)  A summation formula stating that $$\sum_{n=0}^{\infty}f\left(a+n\right)=\int_{a}^{\infty}f\left(x\right)dx+\frac{f\left(a\right)}{2}+\int_{0}^{\infty}\frac{f\left(a-ix\right)-f\left(a+ix\right)}{i\left(e^{2\pi x}-1\right)}dx$$.