Suppose we have $f(z)=\sum\limits_{n=0}^\infty c_nz^n$ for $|z|
Prove that $\frac{1}{2\pi}\int_0^{2\pi}|f(re^{i\theta})|^2d\theta=\sum\limits_{n=0}^\infty|c_n|^2r^{2n}$, $r
Got stuck for this proof ... I have no idea what happens to the series when putting $|f(e^{i\theta})|^2$ under the integral sign ....