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Homework Help: Infinite series, probably related to Fourier transform?

  1. Dec 3, 2012 #1


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    1. The problem statement, all variables and given/known data
    A function f(x) has the following series expansion: ##f(x)=\sum _{n=0}^\infty \frac{c_n x^n}{n!}##.
    Write down the function ##g(y)=\sum _{n=0}^\infty c_n y^n## under a closed form in function of f(x).

    2. Relevant equations
    Not sure at all.

    3. The attempt at a solution
    Totally stuck.
    I've tried to write the first few terms of both series and it basically looks like I'm asked to write a sort of exponential function in terms of a polynomial of infinite degree or something similar to this.
    Really, I think I need a tip because I'm totally stuck. That problem appears after the end of a chapter on integral transforms in Mathews and Walker's book on mathematical methods in physics.
  2. jcsd
  3. Dec 3, 2012 #2


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    The integral transform hint suggests investigating [itex]\int_0^\infty f(x)e^{-xt}dx[/itex]
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