Continuous but nowhere differentiable function
Theorem If $0<\alpha <1$, then the function
Theorem If $0<\alpha <1$, then the function
Definition 1.1 Let $x\in\mathbb{R}$ be a real number. Then
Definition 1.1 A $\mathscr{C}^1$ mapping
Exercise 2.8 Verify that $\frac{1}{2i}\sum_{n\neq 0} \frac{e^{inx}}{n}$ is the Fourier series of the $2\pi$-periodic sawtooth function, defined by $f(0)=0$, ...
Corollary 1.2 (Parseval’s Identity) Let $f$ be integrable function, and $a_n= \hat{f}(n)$. Then $\lim_{N\to\infty}\sum_{n=-N}^N\lvert a_n\rvert^2$ converges ...