Expand in Fourier series:
Expand in fourier sine and fourier cosine series of: f(x) =
x(L-x), 0<x<L
Expand in fourier cosine series: f(x) = sinx, 0<x<pi
Expand in fourier series f(x) = 2pi*x-x^2, 0<x<2pi,
assuming that f is periodic of period 2pi, that is,
f(x+2pi)=f(x)
I know if f(x) is even the fourier series expansion will
consists of consnx, for like f(x)=x^2sinx, or f(x)=2/(3+cosx). but
if the f(x) is neither even or odd, would fourier expansion have
both cosnx and sinnx? This is PDE.