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Fourier series (2 same functions different inequality signs)

  1. Feb 13, 2013 #1
    1. The problem statement, all variables and given/known data

    Untitled.jpg


    these two functions will give the same Fourier series? because when I write the graph they look the same?

    2. Relevant equations



    3. The attempt at a solution

    in the picture

    thank you
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 13, 2013 #2

    jbunniii

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    The series coefficients are defined by an integral. If you change the value of a function at a finite number of points, can the integral give you a different result?
     
  4. Feb 13, 2013 #3
    I think integral give a different result so they are different ? not 100% sure

    because in my lecture note all the example are < ,> there is no single example has <=, >=. so when I tried to do some exercise there are <=, >= on the functions so it kinda confused me. please explain more
     
    Last edited: Feb 13, 2013
  5. Feb 13, 2013 #4

    jbunniii

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    No, you can change a function at a finite number of points, and the integral will still be the same. So your Fourier coefficients will be the same for both functions.
     
  6. Feb 13, 2013 #5
    thank you
     
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