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Homework Help: Exponential function

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

    This topic is under linear system differential equation.Solve the system by using exponential method. Just want to ask the expansion of exponential function

    2. Relevant equations


    3. The attempt at a solution
    then how about the e^(-x)=?
    Besides what is the function of sin x and cos x in continued function (such in e^x)?
  2. jcsd
  3. Aug 1, 2009 #2


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    Homework Helper

    The power series of the exponential, [itex]e^x[/itex], is [itex]\sum_{n=0}^\infty x^n/n![/itex].

    So if you have [itex]e^{-x}[/itex] you can compute the power series by substituting [itex]x \rightarrow -x[/itex] into the power series. Try it out.

    I don't understand your second question. Are you asking for the power series of the sine and cosine? Or for the complex exponential representation?
  4. Aug 1, 2009 #3
    Thanks for the first part.
    I just now find the cosine x can be written in cosine x=1-(x^2)/2!+(x^4)/4!+.....
    I really no idea what this series call for...
    How about the sine x?
  5. Aug 1, 2009 #4


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    It's called the series expansion of the sine/cosine or the power series of the sine/cosine. I would suggest memorizing/deriving the series expansions for the more common functions.

    Check this http://en.wikipedia.org/wiki/Taylor_seriesp [Broken] out for a list of series expansions.
    Last edited by a moderator: May 4, 2017
  6. Aug 1, 2009 #5
    Thanks a lot. You really help me up! =)
    Last edited by a moderator: May 4, 2017
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