By reversing the order of summation in (3.17), show that the generalized cumulant may be written

κ (ϒ

∗) = ∑

Π

κ (π1)…κ (πσ) ∑ (−1)

ν−1

(ν − 1)!.

Hence, using the result of the previous exercise, prove the fundamental identity

(3.3).