1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Infinite series, probably related to Fourier transform?

  1. Dec 3, 2012 #1

    fluidistic

    User Avatar
    Gold Member

    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

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    The integral transform hint suggests investigating [itex]\int_0^\infty f(x)e^{-xt}dx[/itex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Infinite series, probably related to Fourier transform?
Loading...