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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?

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    $\begingroup$ This is more or less a definition of the Bell polynomials. What definition are you working from? $\endgroup$ May 21 '12 at 18:31
  • $\begingroup$ Thanks @Qiachou Yuan, I see it now. $\endgroup$
    – Hans
    Jun 26 '12 at 12:39
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The generating function version can be found in Herb Wilf's book Generatingfunctionology (which is available as a pdf for free, just google it). It is around section 1.6 (among other places, I believe).

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A further reference is:

Comtet, Louis: Advanced combinatorics; the art of finite and infinite expansions. Reidel, 1974.

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