- #1
Ragnord
- 4
- 0
Homework Statement
Find the complex Fourier series for f(t)=t(1-t), 0<t<1
Homework Equations
[tex]\sum_{n=-\infty}^{\infty}c_{n}e^{2in\pi t}[/tex]
where [tex]c_{n}=\int_{0}^{1}f(t)e^{-2in\pi t}dt[/tex]
The Attempt at a Solution
I've worked out that c[tex]_{n}=-1/(2n^2 \pi^2)[/tex]. The problem is that for n=0, it is singular. Is there some way around this or does it mean that the complex Fourier series doesn't exist?
I tried using maple to graph the series with the n=0 term omitted and it comes out to the right shape, but is shifted vertically down some, leading me to believe that the singular term should be replaced by a constant or something.