# Infinite series, probably related to Fourier transform?

1. Dec 3, 2012

### fluidistic

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. Dec 3, 2012

### haruspex

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