Fourier Series

It is well known that an infinitely differentiable function f(x) can be expanded in a Taylor series around a point x0 in the interval where it is defined. This series has the form

f(x) ∼ ∞∑

cn(x − x0)n, (2.1)

where the coefficients cn are given by

cn = f (n)(x0)

n! , n = 1,2, . . . , f (n) =

dnf

dxn .