New posts in Fourier Series

Poisson summation formula clarification regarding Fejer kernel

Why is this allowed? ("Fourier's Trick"; finding the coefficients in a Fourier Series)

Proof of Wirtinger inequality

Showing that $\sum_{k=0}^{\infty} a^{k} \cos(kx) = \frac{1- a \cos x}{1-2a \cos x + a^{2}}$ without using complex variables

Evaluate $\int_{-\pi}^\pi \big|\sum^\infty_{n=1} \frac{1}{2^n} e^{inx}\big|^2 \operatorname d\!x$

Evaluate $\sum^\infty_{n=1} \frac{1}{n^4} $using Parseval's theorem (Fourier series)

Real world application of Fourier series

Is $\sum_{n=1}^{\infty}{\frac{\sin(nx)}n}$ continuous?

The Fejer kernel has this $\sin$ closed form.

How to expand the Fourier series for $f(x)=\max \{0, \frac{\pi}{2}-\lvert x\rvert \} $?