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A power series question

  1. Aug 7, 2005 #1
    Hi

    Just had a question.

    Assuming tan(x) is given by a power series with coefficiants (An). How can it be shown that An = 0 whenever n is even.



    Thanks
     
  2. jcsd
  3. Aug 7, 2005 #2

    LeonhardEuler

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    Gold Member

    I assume you mean a power series centered about x=0. tan(x) is an odd function, i.e. tan(-x)=-tan(x). If it had nonzero coefficients to its even powered terms this could not be the case.
     
  4. Aug 7, 2005 #3
    thanks a lot :)
     
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