2.6.2.13 Trigonometric Fourier series

Problem: Expand function \( f(x) \) into the trigonometric Fourier series in \( [-\pi ; \pi] \), continuing function in \( [-\pi ; 0] \) evenly. \[ f(x)=\left\{\begin{array}{ll} x-\frac{\pi}{2}, & 0 \leq x \leq \frac{\pi}{2} \\ 2 x-\pi, & \frac{\pi}{2} \leq x \leq \pi \end{array}\right. \]