Fourier Sine Series

Definition

$f(x)\sim \sum _{n=1}^{\infty }{b}_n\sin (nx)$

Given $f\in C_p(0,\pi )$^[Piecewise Continuous], an infinite series $\sum _{n=1}^{\infty }{b}_n\sin (nx),b_n=\frac{2}{\pi }{\int }_0^{\pi }f(x)\sin (nx)dx,{}_{(n=0,1,2)}$ is called the Fourier sine series representation for $f$.