A more accurate approximation for the gamma function

JOURNAL OF NUMBER THEORY

卷:164

Article

Chen, Chao-Ping¹ 

[1] Henan Polytech Univ, Sch Math & Informat, Jiaozuo City 454000, Henan Province, Peoples R China

关键词: Gamma function;    Inequality;    Approximation;    Asymptotic expansion;   

DOI  :  10.1016/j.jnt.2015.11.007

来源: Elsevier

【 摘 要 】

In this paper, we establish a double inequality for the gamma function, from which we deduce the following approximation formula: Gamma(x + 1) similar to root 2 pi x (x/e)(x) (1 + 1/12x(3) + 24/7x - 1/2)(x2) (+) (53/210), x ->infinity, which is more accurate than the Burnside, Gosper, Ramanujan, Windschitl, and Nemes formulas. We develop the previous approximation formula to produce an asymptotic expansion. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free