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Partial fraction decomposition with complex function

  1. Apr 26, 2012 #1
    As part of a project I have been working on I fin it necessary to manipulate the following expression.

    e^(icx)/(x^2 + a^2)^2 for a,c > 0

    I would like to decomp it into the form

    A/(x^2 + a^2) + B/(x^2 + a^2) = e^(icx)/(x^2 + a^2)^2

    but I am having trouble getting a usable outcome.
     
  2. jcsd
  3. Apr 26, 2012 #2
    You need to apply laplace's transform to this to solve for this. you have the write set up, BUT

    A/(x^2+a^2) + B/((x^2+a^2)^2), look up laplace transforms and do it as so... you can solve it then.

    Yus310
     
  4. Apr 26, 2012 #3

    No wonder you're having problems: it can't be done, as your function is a transcendental function (i.e., [tex]e^{icx}[/tex] is NOT a polynomial, whereas the sum of fractions you want is a rational function.

    DonAntonio
     
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