CentralMomentGeneratingFunction

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

CentralMomentGeneratingFunction[dist, {t1, t2, ...}] gives the central moment-generating function for a multivariate distribution.

Examples

Central moment-generating function for a normal distribution:

CentralMomentGeneratingFunction[NormalDistribution[μ, σ], t]
(* E^((σ^2*t^2)/2) *)

For a Poisson distribution:

CentralMomentGeneratingFunction[PoissonDistribution[λ], t]

Please visit the official Wolfram Language Reference for more details.