Let M(h) be the moment-generating function, then the cumulant generating function is given by K(h) | congruent | ln M(h) | = | κ_1 h + 1/(2!) h^2 κ_2 + 1/(3!) h^3 κ_3 + ..., where κ_1, κ_2, ..., are the cumulants.

cumulant | moment-generating function