Sharp Smith’s bounds for the gamma function

نویسندگان

  • Xi-Qiao Li
  • Zhi-Ming Liu
  • Zhen-Hang Yang
  • Shen-Zhou Zheng
چکیده

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.

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عنوان ژورنال:

دوره 2018  شماره 

صفحات  -

تاریخ انتشار 2018