Open AccessComplete asymptotic expansions related to the probability density function of the χ2-distribution
Author(s) -
Chao-Ping Chen,
H. M. Srivástava
Publication year - 2022
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm210720015c
Subject(s) - mathematics , asymptotic expansion , integer (computer science) , probability density function , function (biology) , asymptotic formula , combinatorics , distribution (mathematics) , distribution function , mathematical analysis , pure mathematics , statistics , quantum mechanics , physics , evolutionary biology , computer science , biology , programming language
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.