Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (2): 511-520.doi: 10.1007/s10473-022-0206-9

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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).

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

CLC Number: 

  • 26A48
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