Half range Fourier series

A half range Fourier series is a Fourier series defined on an interval $[0,L]$ instead of the more common $[-L,L]$, with the implication that the analyzed function $f(x),\; xin\; [0,L]$ should be extended to $[-L,0)$ as either an even or odd function. This allows the expansion of the function in a series solely of sines (odd) or cosines (even). The choice between odd and even is typically motivated by boundary conditions associated with a differential equation satisfied by $f(x)$.