与χ2分布的概率密度函数相关的完全渐近展开式

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 DOI:10.2298/aadm210720015c

Chao Chen, H. Srivastava

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引用次数: 0

摘要

本文考虑函数fp(t) = ?2 p 2 (?2 pt + p, p)在哪里? 2 (x; n)定义的? 2 (x, p) = 2 ? p / 2 / ? ? (p / 2) e x / 2 xp / 2 ?1，是n个自由度的?2分布的密度函数。p(t)的渐近展开式其中p不一定是整数，它是通过应用ln ?(x)的标准渐近得到的。给出了两种不同的求渐近展开系数的方法，这两种方法都涉及到贝尔多项式的使用。

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Complete asymptotic expansions related to the probability density function of the χ2-distribution

In this paper, we consider the function fp(t) = ? 2p?2(?2pt + p;p), where ?2(x;n) defined by ?2(x;p) = 2?p/2/?(p/2) e?x/2xp/2?1, is the density function of a ?2-distribution with n degrees of freedom. The asymptotic expansion of fp(t) for p ? ?, where p is not necessarily an integer, is obtained by an application of the standard asymptotics of ln ?(x). Two different methods of obtaining the coefficients in the asymptotic expansion are presented, which involve the use of the Bell polynomials.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.