So I have a bit of confusion regarding the coefficients of a fourier series. On an interval from $[-L,L]$ some places state that:
$$a_n=\frac{1}{L}\int_{-L}^{L}f(x)\cos\left(\frac{n \pi x}{L} \right)dx, n=0,1,2,3,...$$
$$b_n=\frac{1}{L}\int_{-L}^{L}f(x)\sin\left(\frac{n \pi x}{L} \right)dx, n=0,1,2,3,...$$
$$a_o=\frac{1}{L}\int_{-L}^{L}f(x)dx$$
However, in other places, I have that:
$$a_o=\frac{1}{2L}\int_{-L}^{L}f(x)dx$$
For instance, This link vs this link.
Which one is correct? I am a little confused about that. if someone could clarify, that would be awesome!