Fourier Series for Even Functions
For an even function f(t), defined over the range -L to L (i.e. period = 2L), we have the following handy short cut.
f(t) is even,it means the integral will have value 0. (See Properties of Sine and Cosine Graphs.)
So for the Fourier Series for an even function, the coefficient bn has zero value:
bn = 0So we only need to calculate a0 and an when finding the Fourier Series expansion for an even function f(t):
An even function has only cosine terms in its Fourier expansion:
Specally how he has written ao/2 in last equation. Thanks