Abel-Plana formula

English

Etymology

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

Proper noun

1. Template:Lb A summation formula stating that $\sum _{n=0}^{\mathrm{\infty }}f(a+n)=\underset{a}{\overset{\mathrm{\infty }}{\int }}f\left(x\right)dx+\frac{f\left(a\right)}{2}+\underset{0}{\overset{\mathrm{\infty }}{\int }}\frac{f(a-ix)-f(a+ix)}{i(e^{2\pi x}-1)}dx$.