Fourier Series?

Question

Find the Fourier Series of the following:

f(t) = t^2, 0 <= t < 2 pi

I got:

a0 = 8*pi^2 / 3

an = 4 / n^2

bn = -4*pi / n

This is the same as the book, except they have: an = -4 / n

Is the book incorrect or am I?

thanx.

Answer 1

When I calculate:

2/T * Integral[ f(t) * sin(2*pi*n*t/T), t, 0, T]

I get this:

-4*pi / n

I did this in Mathematica, which is not known for making mistakes on integrals like these, so I'd say your book has a typo.