Factorial moment generating function

In probability theory and statistics, the factorial moment generating function (FMGF) of the probability distribution of a real-valued random variable X is defined as M X ( t ) = E ⁡ [ t X ] {\displaystyle M_{X}(t)=\operatorname {E} {\bigl [}t^{X}{\bigr ]}} for all complex numbers t for which this expected value exists. This is the case at least for all t on the unit circle | t | = 1 {\displaystyle |t|=1} , see characteristic function.

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