First of all sorry for my stupidity. I am learning to find Fourier Series coefficient as fast a possible for my exam. But it's getting really confusing deriving a factor.
For example: In one website, I see the formula derived for $a_0$:
On the other hand, I see the formula derived for $a_0$:
Where both function are of the period $2\pi$ and on interval $\left\[-\pi, \pi\right\]$.
It would be really appreciable, if somebody would explain me how the factor in one formula is $1/\pi$ and $1/2\pi$ in another one.
Essentially they are both equivalent. It's just that some literature defines a Fourier series $S(x)$ by
$$S(x)=\frac{a_0}{2}+...$$
and other literature defines it as$$S(x)=a_0+...$$