Recent questions tagged fourier-series

Periodic function $f(x)$ is given below.\[f(x)=\left\{\begin{array}{lll}-1, & \text{when} & -\pi < x < 0 \\1, & \text{when} & 0 < x < \pi\end{array}\right\};\; f(x+2\pi)...

The Fourier series to represent $x- x^2$ for $-\pi\leq x\leq \pi$ is given by$$ x-x^2 = \dfrac{a_0}{2} + \sum_{n=1}^{\infty} a_n\ \cos nx + \sum_{n=1}^{\infty} b_n\ \si...

The Fourier series of the function,$\begin{array}{rll} f(x) & =0, & -\pi < x \leq 0 \\ {} & =\pi – x, & 0 < x < \pi \end{array}$in the interval $[- \pi, \pi ]$ is$f(x) = ...