数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (2): 511-520.doi: 10.1007/s10473-022-0206-9

• 论文 • 上一篇    下一篇

COMPLETE MONOTONICITY FOR A NEW RATIO OF FINITELY MANY GAMMA FUNCTIONS

祁锋1,2   

  1. 1. Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, China;
    2. School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
  • 收稿日期:2020-02-24 修回日期:2021-07-22 出版日期:2022-04-25 发布日期:2022-04-22
  • 作者简介:Feng QI,E-mail:qifeng618@yeah.net,qifen618@gmail.com,qifeng618@hotmail.com
  • 基金资助:
    This work was partially supported by the National Nature Science Foundation of China (12061033).

COMPLETE MONOTONICITY FOR A NEW RATIO OF FINITELY MANY GAMMA FUNCTIONS

Feng QI1,2   

  1. 1. Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, China;
    2. School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
  • Received:2020-02-24 Revised:2021-07-22 Online:2022-04-25 Published:2022-04-22
  • Supported by:
    This work was partially supported by the National Nature Science Foundation of China (12061033).

摘要: In this paper, by deriving an inequality involving the generating function of the Bernoulli numbers, the author introduces a new ratio of finitely many gamma functions, finds complete monotonicity of the second logarithmic derivative of the ratio, and simply reviews the complete monotonicity of several linear combinations of finitely many digamma or trigamma functions.

关键词: Bernoulli number, ratio, generating function, complete monotonicity, gamma function, digamma function, trigamma function, logarithmic derivative, linear combination, inequality

Abstract: In this paper, by deriving an inequality involving the generating function of the Bernoulli numbers, the author introduces a new ratio of finitely many gamma functions, finds complete monotonicity of the second logarithmic derivative of the ratio, and simply reviews the complete monotonicity of several linear combinations of finitely many digamma or trigamma functions.

Key words: Bernoulli number, ratio, generating function, complete monotonicity, gamma function, digamma function, trigamma function, logarithmic derivative, linear combination, inequality

中图分类号: 

  • 26A48