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Power Series expansion of hyperbolic functions

  1. Feb 1, 2009 #1
    1. The problem statement, all variables and given/known data

    power series expansion of:

    ((cosh x)/(sinh x)) - (1/x)


    2. Relevant equations

    cosh x = (1/2)(ex + e-x)
    sinh x = (1/2)(ex - e-x)

    3. The attempt at a solution
    what i have so far:

    I simplified the first part of the eq to read :
    e2x-1
    e2x-1


    now I am stuck. please help
     
  2. jcsd
  3. Feb 1, 2009 #2
    You simplified for it to be [tex] \frac{e^{2x}-1}{e^{2x}-1} [/tex]? Isn't that just 1?
     
  4. Feb 1, 2009 #3

    mjsd

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    error in simplification:

    [tex]\frac{e^{2x}+1}{e^{2x}-1}[/tex]
     
  5. Feb 1, 2009 #4
    I'm sorry that was a typo. Should I just expand both was like you would ex? how about the 1/x part?
     
  6. Feb 1, 2009 #5
    I would and then hopefully things will cancel, for example what's the expansion for [tex]e^{2x} - 1 [/tex]?
     
  7. Feb 2, 2009 #6

    mjsd

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    How do one usually find the taylor series of a given function?
    now you have a function, what do you do? :rolleyes:
     
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