Compute the Fourier Sine series of the odd function: $f(x) = x^3 - 4x, -2 \leq x \leq 2 $. (Periodically extended with period 4)
I know how to compute this of course where: $b_n = \int_{0}^{2}f(x)*sin(\frac{n\pi}{2}x)dx$. But it'd be a tedious integration by parts question a bunch of time. I was told there is a much faster way of integrating this by using a "Moment Generating Function" and take the Taylor expansion to n = 3. But I don't understand how that works.
Any sort of explanation for it?
Thank you!