New posts in Fourier Series

Prove $\sum_{k=0}^n\binom{n}{k}\cos\left(\frac{k\pi}{2} - \frac{n\pi}{4}\right) = \sqrt{2^n}$

Show that the sum of a function series is bounded

ODE $f''''(x)+f(x) = \cos{x} - \left( \sin{x} \right)^2$ with boundary conditions $f(0)=f(\pi); \quad \quad f'(0)=f'(\pi)$

How can you approach $\int_0^{\pi/2} x\frac{\ln(\cos x)}{\sin x}dx$

Showing that $\int_{-\infty}^{\infty}\frac{x^2}{(x^2+a^2)(x^2+b^2)}dx=\frac{\pi}{a+b}$ via Fourier Transform

Show that $f_{k}\longrightarrow f$ both weakly in $L^{p}$ and a.e. implies $|f_{k}|^{p}-|f|^{p}-|f_{k}-f|^{p}$ converges to $0$ in distribution

Asymptotic expansion of $f(x)=\sum _{n=1}^{\infty } \frac{\sin \left(\sqrt{n}x\right)}{n}$ at the origin

Differentiability of $\sum_{k=0}^{\infty}c_{k}e^{ikt}$ given $\lim_{k\to\infty}k^{m}c_{k}=0$

About Rudin's outline to proving that Lipschitz functions have converging Fourier Series

What functions can be represented as a series of eigenfunctions