FactorialMomentGeneratingFunction

FactorialMomentGeneratingFunction[dist, t] gives the factorial moment-generating function for the distribution dist as a function of t.

Examples

Factorial MGF of Poisson distribution:

FactorialMomentGeneratingFunction[PoissonDistribution[λ], t]
(* E^(λ (-1 + t)) *)

For binomial distribution:

FactorialMomentGeneratingFunction[BinomialDistribution[n, p], t]

Please visit the official Wolfram Language Reference for more details.