Generating Function for Elementary Symmetric Function/Proof 1

Proof
The summation for $\map G z$ is a finite sum $m = 0,\ldots,n$, which settles convergence issues.

Begin with Viete's Formulas:


 * $\displaystyle \prod_{k=a}^b \paren { x - x_k } = x^n + \sum_{m \mathop = 0}^{n-1} \map {e_{n-m} } U \, x^m$

Change variables $x = -1/z$: