COMPLETE MONOTONICITY FOR A NEW RATIO OF FINITELY MANY GAMMA FUNCTIONS

doi:10.1007/s10473-022-0206-9

摘要/Abstract

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

祁锋. COMPLETE MONOTONICITY FOR A NEW RATIO OF FINITELY MANY GAMMA FUNCTIONS[J]. 数学物理学报(英文版), 2022, 42(2): 511-520.

Feng QI. COMPLETE MONOTONICITY FOR A NEW RATIO OF FINITELY MANY GAMMA FUNCTIONS[J]. Acta mathematica scientia,Series B, 2022, 42(2): 511-520.

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