Error bounds and exponential improvement for Hermite's asymptotic expansion for the Gamma function

Applicable Analysis and Discrete Mathematics

article

Gergő Nemes¹ 

[1] Central European University, Department of Mathematics and its Applications

关键词: Asymptotic expansions;    Error bounds;    Gamma function;   

DOI  :  10.2298/AADM130124002N

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 】

In this paper we reconsider the asymptotic expansion of the Gamma functionwith shifted argument, which is the generalization of the well-known Stirlingseries. To our knowledge, no explicit error bounds exist in the literature forthis expansion. Therefore, the first aim of this paper is to extend the knownerror estimates of Stirling’s series to this general case. The second aim is togive exponentially-improved asymptotics for this asymptotic series.

【 授权许可】

Unknown