f(x) = x.sin(x)
TheFourier series for f(x) = x.sin(x) is given by
s(x) = a0/2 + Sum[n=1 to infinity]{a_n.cos(nx) + b_n.sin(x)}
where
a_n = (1/pi)*int[0 .. 2pi] f(x).cos(nx) dx, (n >= 0)
b_n = (1/pi)*int[0 .. 2pi] f(x).sin(nx) dx, (n >= 1)
Evaluating the above coefficients for n = 0 to 3 gives us,
a0 = -2
a1 = -1/2 b1 = pi
a2 = 2/3 b2 = 0
a3 = 1/4 b3 = 0
The fourier series for f(x) = x.sin(x) is
s(x) = -1 - (1/2)cos(x) + pi.sin(x)+ (2/3)cos(2x) + (1/4)cos(3x) + ...