Geodesic
Approximation of the moments of arbitrary integer orders of generalized factorial powers
Diskretnaya Matematika, Tome 17 (2005) no. 1, pp. 50-67 
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/
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     title = {Approximation of the moments of arbitrary integer orders of generalized factorial powers},
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     url = {http://geodesic.mathdoc.fr/item/DM_2005_17_1_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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