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: Fourier series convergence question

  1. Sep 9, 2011 #1
    1. The problem statement, all variables and given/known data

    f(x) = 5, -pi <= x <= 0
    f(x) = 3, 0 < x <= pi

    f(x) is the function of interest

    Find the x-points where F(x) fails to converge
    to f(x)

    2. Relevant equations

    F(x) = f(x) if f is continuous at [itex]x\in(-L,L)[/itex]
    F(x) = 0.5[ f(x-) + f(x+) ] if f is discontinous at [itex]x\in(-L,L)[/itex]

    F(x) is the fourier series of f(x)

    3. The attempt at a solution

    Would the Fourier series, F(x) fail to converge
    at +pi and -pi ?

    My reasoning is as follows

    - At both -pi and +pi, we have the start and end value of f(x)

    - By definition F(x) = (1/2)f(x-) + (1/2)f(x+)

    - Lets take x = -pi, which means f(x) =5 and f(-x) = 3

    - F(-pi) = (1/2)(5) + (1/2)(3) = 8/2 = 4 which is not equal to f(-pi)=5

    - From the latter, we can conclude that F(-pi) fails to converge to
    the value given from f(-pi) since their not equal to each other

    Just want to check if my reasoning is ok since no answer was provided to this question

  2. jcsd
  3. Sep 9, 2011 #2
    Seems ok...
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook