Half range Fourier series

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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 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).