# Exponential of formal power series and Bell polynomials

Wikipedia gives here the following formula for the exponential of a formal power series:

$\exp \Big[\ \sum_{n=1}^\infty \frac{a_n}{n!} x^n\ \Big] = \sum_{n=0}^\infty \frac{B_n(a_1,\dots,a_n)}{n!} x^n$

where $B_n$ are (complete) Bell-polynomials. Can anybody give me a ("standard") reference for this?

• This is more or less a definition of the Bell polynomials. What definition are you working from? May 21 '12 at 18:31
• Thanks @Qiachou Yuan, I see it now.
– Hans
Jun 26 '12 at 12:39