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Developping sin(x) on [0, pi] as a serie of cosines

  1. Sep 15, 2005 #1

    quasar987

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    Am I crazy or this is impossible to do if we require that the period of the extended even function be 2pi ?

    Yet, this question comes in my textbook before the section concerning Fourier extension of functions of period other than 2pi. So there must be a way?
     
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  3. Sep 15, 2005 #2

    LeonhardEuler

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    I'm pretty sure it's possible. Extend sin(x) before x=0 as -sin(x) so the function is even. Now do a cosine series on the interval [-pi,pi] and it will be valid on [0,pi] and have period 2pi.
     
  4. Sep 15, 2005 #3

    quasar987

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    This is what I did, but the period of this function (|sin(x)|) is pi.
     
  5. Sep 15, 2005 #4

    quasar987

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    Arr, you're right.
     
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