A function is defined over (0, 2) by
f(x) = 1/4x + 1.
We then extend it to an even periodic function of period 4 and its graph is displayed below.
The function may be approximated by the Fourier series
f(x) = a0 + sum(n=1 to infinity, an cos(n*pi*x/L) + bn sin(n*pi*x/L))
where L is the half-period of the function.
Use the fact that f(x) sin(n*pi*x/L) is an odd functions, enter the value of bn in the box below.
bn =
for n = 0, 1, 2, ...
Hence besides the constant term, the Fourier series made up entirely of cosines.
Calculate the following coefficients of the Fourier series and enter them below in Maple syntax.
a0 =
a2k-1 =
a2k =
for k = 1, 2, ...