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!

The Fourier Series

  1. Nov 27, 2009 #1
    1. The problem statement, all variables and given/known data

    f(x) = 1 0<t<1
    = -1 1<t<2

    How can I simplify this given that function(on the attachment).

    What I mean is that how can I write the function in any other way?

    In addition, How can I know if the function can be written in other form?
    How can I write the function in other form?



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Nov 27, 2009 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    If n is even, 1- (-1)n= 1- 1= 0! If n is odd, 1- (-1)n= 1- (-1)= 2.

    So
    [tex]\frac{2}{\pi}\sum_{n=1}^\infty \frac{[1- (-1)^n] sin(n\pi t)}{n}[/tex]
    is just
    [tex]\frac{2}{\pi}\sum \frac{2 sin(n\pi t)}{n}[/tex]
    where now the sum runs only over odd n. One way to show that is to use 2n+1 rather than n in the body of the sum. That way, as n goes over all non-negative integers, 2n+1 goes over all positive odd integers:
    [tex]\frac{4}{\pi}\sum_{n=0}^\infty \frac{sin((2n+1)\pi t)}{2n+1}[/tex]
     
  4. Nov 27, 2009 #3
    Can 2n+1 be 2n-1 provided that n=1 to infinity?
    How can I know if the function can be converted in some form?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: The Fourier Series
  1. Fourier Series (Replies: 1)

  2. Fourier series (Replies: 10)

  3. Fourier Series (Replies: 1)

  4. Fourier Series (Replies: 6)

Loading...