I've been reading up on the Fourier Series and have come across formulae for the coefficients. In my notes, I have the following formula
$$a_n=1/\pi\int_{-\pi}^{\pi} f(x)cos(nx)dx$$ for n=0,1,2,3,4...
From this I can derive a_0, (cos(0x)=1), $$a_0=1/\pi\int_{-\pi}^{\pi} f(x)dx$$
However, in most other places, a direct a_0 formula is given like this, $$a_0=1/2\pi\int_{-\pi}^{\pi} f(x)dx$$
My question is how come in some places it's 1/2pi and in other places they don't provide a formula for it and you can derive it using the a_n formula which ends up to give you 1/pi