In several texts, I see that the Fourier series of a function $f=f(t)$ with period $2L$ is defined by
$Sf(t):=a_0+\sum_{n=1}^{\infty}\left[a_n\cos\frac{n\pi t}{L}+b_n\sin\frac{n\pi t}{L}\right]$
I wonder why this is not written this way instead:
$Sf(t):=\sum_{n=0}^{\infty}\left[a_n\cos\frac{n\pi t}{L}+b_n\sin\frac{n\pi t}{L}\right]$
Thanks in advance for the clarification.