Chapter 7.11, Problem 3P

If $f(x)$ is complex, we usually want the average of the square of the absolute value of $f(x)$.

Recall that $|f(x){|}^2=f(x)\cdot \bar{f}(x),$ where $\bar{f}(x)$ means the complex conjugate of $f(x).$ Show that if a complex $f(x)={\displaystyle \underset{-\infty }{\overset{\infty }{\sum }}{c}_n}{e}^{in\pi x/l},$ then ( 11.5) holds.