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Series representation help

  1. Jul 24, 2009 #1
    Does anyone know of a series representation for:


    Preferably valid for 0<x, but any ideas or assistance on any domain would be much appreciated.
  2. jcsd
  3. Jul 24, 2009 #2
    Do a taylor series, for sin(x), cos(x), cosh(x), 1/x, then compose them and use the multinational theorm.
  4. Jul 24, 2009 #3


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    You could cancel some of the terms on denominator to get [tex]1+\frac{x^{4}}{4!}+\frac{x^{8}}{8!}+...=\sum_{n=0}^{\infty}\frac{x^{4n}}{(4n)!}[/tex] and then do long division.

    Wolfram Alpha gives
    Last edited: Jul 24, 2009
  5. Jul 25, 2009 #4
    And Maple disagrees in some signs...
    [tex]{\frac {\sin \left( x \right) }{\cos \left( x \right) +\cosh \left( x
    \right) }} = {\frac {1}{2}}x-{\frac {1}{12}}{x}^{3}-{\frac {1}{60}}{x}^{5}+{\frac
    {17}{5040}}{x}^{7}+{\frac {31}{45360}}{x}^{9}-{\frac {691}{4989600}}{x
    }^{11}+O \left( {x}^{12} \right)
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