Examples

2.2 (b) PROBLEMS UNDER THE INTERVAL (−l, l)|

Example 2.2.b(1): If f(x) = x is defined in -/ < x < / with period 2l, find the Fourier expansion of f(x).

Solution :

f(x) = x

f(-x) = -x = -f(x)

Therefore f(x) is an odd function. Hence a₀ = 0 and a_n = 0

Let the required Fourier series be

Example 2.2.b(2): Obtain the Fourier series for the function given by

Example 2.2.b(3) Expant f(x) = e^-x as Fourier series in (-1,1)

Example 2.2.b(4) Find the Fourier series expansion of the periodic function

Example 2.2.b(5): Find the Fourier series expansion the following