1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Complex Fourier series has a singular term

  1. Apr 5, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the complex Fourier series for f(t)=t(1-t), 0<t<1

    2. Relevant 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]

    3. 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.
  2. jcsd
  3. Apr 6, 2009 #2
    [tex] c_0=\int_0^1 f(t)\,dt [/tex]
  4. Apr 6, 2009 #3
    Well that was easy, just like a real Fourier series. Thanks.
    I'm interested in knowing why that's the case though, I haven't seen anything about doing anything special for [tex] c_{0} [/tex] in anything I've seen about complex Fourier series.
  5. Apr 7, 2009 #4
    Just plug in n=0 before integrating instead of after!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook