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Finding a power series expansion for a definite integral

  1. Mar 12, 2012 #1
    1. The problem statement, all variables and given/known data

    Find a power series expansion about x = 0 for the function

    f(x) = [itex]^{1}_{0}\int\frac{1 - e^{-sx}}{s}[/itex] ds

    2. Relevant equations

    The power series expansion for a function comes of the form f(x) = [itex]^{\infty}_{0}\sum a_{k}x^{k}[/itex]

    3. The attempt at a solution

    I've tried several things to start off with but quickly end up hitting a dead end road. First, I tried just simply taking the integral, but quickly found it isn't defined at 0 (hence why they are asking me to find a power series expansion for it). Then, I tried finding a power series expansion for the innerpart of the integral and ran into the same problem.
  2. jcsd
  3. Mar 12, 2012 #2


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    Did you try substituting the Taylor series (as a function of x) for ##e^{-sx}## in the integrand, simplifying and integrating?
  4. Mar 13, 2012 #3
    Yeah, I figured that out shortly after I posted this. Can't believe I overlooked that! Thanks!
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