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In the mathematical theory of probability, the combinants cn of a random variable X are defined via the combinant-generating function G(t), which is defined from the moment generating function M(z) as G X ( t ) = M X ( log ⁡ ( 1 + t ) ) {\displaystyle G_{X}(t)=M_{X}(\log(1+t))} which can be expressed directly in terms of a random variable X as G X ( t ) := E [ ( 1 + t ) X ] , t ∈ R , {\displaystyle G_{X}(t):=E\left[(1+t)^{X}\right],\quad t\in \mathbb {R} ,} wherever this expectation exists.

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