Definition
For any formal power series of the form
we have
where
and the index π runs through the list of all partitions { S1, ..., Sk } of the set { 1, ..., n }. (When k = 0, the product is empty and by definition equals 1.)
One can write the formula in the following form:
and thus
where Bn(a1, ..., an) is the nth complete Bell polynomial.
Read more about this topic: Exponential Formula
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