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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

    thanks
     
  2. jcsd
  3. Sep 9, 2011 #2

    micromass

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    Seems ok...
     
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