Parseval’s Equation

Definition

$||f|{|}^2=\underset{N\to \infty }{\lim }{\sum }_{n=1}^N{c}_n^2=\underset{N\to \infty }{\lim }||{\sum }_{n=1}^N{c}_n{\varphi }_n|{|}^2$

Facts

Parseval’s equation is a sufficient and necessary condition for orthonormal set to be complete