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?

    

   quasar987, Sep 15, 2005
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3. Sep 15, 2005 #2

   LeonhardEuler

   

   Gold Member

   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.

    

   LeonhardEuler, Sep 15, 2005
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.

    

   quasar987, Sep 15, 2005
5. Sep 15, 2005 #4

   quasar987

   

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   Arr, you're right.

    

   quasar987, Sep 15, 2005

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