Expectation values for integer powers of a Poisson-distributed random number.

IF 1.8 4区材料科学

Acta Crystallographica Section A Pub Date : 2012-11-01 Epub Date: 2012-09-07 DOI:10.1107/S010876731203200X

Julian Henn

引用次数: 1

Abstract

It is shown that expectation values of Poisson-distributed random numbers exist not only for the well known positive integer powers but also for negative integer powers. A recursion formula for the calculation of expectation values of powers differing by one is given. This recursion formula helps to find an analytical representation for both positive and negative integer powers in terms of the hypergeometric function.

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泊松分布随机数的整数幂的期望值。

证明了泊松分布随机数的期望值不仅对正整数幂存在，而且对负整数幂也存在。给出了幂差为1的期望值的递推计算公式。这个递推公式有助于找到超几何函数中正负整数幂的解析表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Crystallographica Section A 化学-晶体学

自引率

11.10%

发文量

审稿时长

3 months

期刊介绍： Acta Crystallographica Section A: Foundations and Advances publishes articles reporting advances in the theory and practice of all areas of crystallography in the broadest sense. As well as traditional crystallography, this includes nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies and the structure of strain and defects in materials. The journal has two parts, a rapid-publication Advances section and the traditional Foundations section. Articles for the Advances section are of particularly high value and impact. They receive expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details are given in the November 2013 Editorial. The central themes of the journal are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements.