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Inverse laplace and power series

  1. Sep 22, 2009 #1
    1. The problem statement, all variables and given/known data

    I am trying to figure out how to represent an inverse laplace transform by a power series. There is an example in my book but it is not very well explained.

    f(s)=1/s+1 which i know is the transform of y=e^-t.

    In the book they use the fact that L(t^n)= n!/s^n+1. and therefore a taylor series representation given by t^n/n!=the inverse of 1/s^n+1. Therefore our power series in s has this form. After this point i am totally lost. They state that 1/s+1 =1/s(1+1/s).
    and the solution is therfore (1/s)-(1/s^2)+(1/s^3) etc.

    Now id like to know, WHY do they take the factor of s out of the equation?
    ANd then how do they find the coefficients of the s terms? do they differentite f(s) to find the coefficient of each s term? like we do for a taolr series
    Is there an easier way?
    and waht value of s, is it evaluated at to find the coefficients?
    If someone understands this i would appreciate an explanation, because this book seems to always assume that the reader is a 20 year mathematics veteran or something!
    So please dont just post the answer because i already know the answer, i am trying to understand this concept.


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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