Fourier cosine coefficient
= Fourier cosine coefficient
{c}
{title2=$a_n=\frac2L\int_0^Lf(x)\cos(n\pi x/L)dx$}
On $[0,L]$, the <Fourier cosine series> convention $f(x)=a_0/2+\sum_{n\geq1}a_n\cos(n\pi x/L)$ uses the displayed coefficients, including $n=0$. <Orthogonality> of the <cosine> modes gives these formulas for <square-integrable functions>; the expansion is interpreted in the <L2 norm> until stronger convergence is established.