Complete asymptotic expansions related to the probability density function of the $chi^{2}$-distribution

Applicable Analysis and Discrete Mathematics

article

Chao-Ping Chen¹  H. M. Srivastava² 

[1] School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City 454000, Henan Province;Department of Mathematics and Statistics, University of Victoria;Department of Medical Research, China Medical University Hospital, China Medical University;Azerbaijan University;Section of Mathematics, International Telematic University Uninettuno

关键词: Gamma function;    χ2-Distribution;    Probability density function;    Asymptotic expansion;    Bell polynomials;    Bernoulli numbers;   

DOI  :  10.2298/AADM210720015C

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

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 Γ(x). Two different methods of obtaining the coefficients in the asymptotic expansion are presented, which involve the use of the Bell polynomials.

【 授权许可】

Unknown