Fourier Series Exam Notes

f[x] defined on [-L, L] has Fourier series

((a[0])/2) + (∑_(n=1)^∞)( a[n] Cos[((n π x)/L)] + b[n] Sin[((n π x)/L)])
where 
a[n] = (1/L) (∫_(-L)^L) f[x]Cos[((n π x)/L)]dx  , n= 0,1, 2, ...
b[n] = (1/L) (∫_(-L)^L) f[x]Sin[((n π x)/L)]dx  , n= 1, 2, ...

f[x] defined on [0, L] has Fourier cosine series

((a[0])/2) + (∑_(n=1)^∞)a[n] Cos[((n π x)/L)]
where   a[n] = (2/L) (∫_0^L) f[x]Cos[((n π x)/L)]dx  , n= 0,1, 2, ...