Li Xi-Qiao, Liu Zhi-Ming, Yang Zhen-Hang, Zheng Shen-Zhou
1School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China.
Department of Science and Technology, State Grid Zhejiang Electric Power Company Research Institute, Hangzhou, China.
J Inequal Appl. 2018;2018(1):27. doi: 10.1186/s13660-018-1620-3. Epub 2018 Jan 31.
Among various approximation formulas for the gamma function, Smith showed that [Formula: see text] which is a little-known but accurate and simple one. In this note, we prove that the function [Formula: see text] is strictly increasing and concave on [Formula: see text], which shows that Smith's approximation is just an upper one.
在伽马函数的各种近似公式中，史密斯证明了[公式：见原文]，这是一个鲜为人知但准确且简单的公式。在本笔记中，我们证明函数[公式：见原文]在[公式：见原文]上严格递增且为凹函数，这表明史密斯的近似只是一个上界近似。
