Geodesic
Approximation of the moments of arbitrary integer orders of generalized factorial powers
Diskretnaya Matematika, Tome 17 (2005) no. 1, pp. 50-67

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For non-negative integer random variables $\xi$, we consider approximations of the moments $\boldsymbol{\mathsf E}\xi^m$, where $m$ are integers, including negative integers. We find estimates of the difference $$ \boldsymbol{\mathsf E}\xi^m - \sum_{k=0}^s\genfrac{\{}{\}}{0mm}{}m{m-k}\boldsymbol{\mathsf E}\xi^{\underline {m-k}}, $$ where $\genfrac{\{}{\}}{0mm}{}m{m-k}$ are extensions to all integers $m$ of Stirling numbers of the second kind, the functions $ x^{\underline m}$ are the generalised factorial powers, and $s$ is a positive integer. 
@article{DM_2005_17_1_a4,
     author = {A. P. Baranov and Yu. A. Baranov},
     title = {Approximation of the moments of arbitrary integer orders of generalized factorial powers},
     journal = {Diskretnaya Matematika},
     pages = {50--67},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2005_17_1_a4/}
}
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A. P. Baranov; Yu. A. Baranov. Approximation of the moments of arbitrary integer orders of generalized factorial powers. Diskretnaya Matematika, Tome 17 (2005) no. 1, pp. 50-67. http://geodesic.mathdoc.fr/item/DM_2005_17_1_a4/