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COMPLETE MONOTONICITY FOR A NEW RATIO OF FINITELY MANY GAMMA FUNCTIONS

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【作者】 祁锋；

【Author】 Feng QI;Institute of Mathematics,Henan Polytechnic University;School of Mathematical Sciences,Tiangong University;

【机构】 Institute of Mathematics,Henan Polytechnic University； School of Mathematical Sciences,Tiangong University；

【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.

【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.

【关键词】 Bernoulli number； ratio； generating function； complete monotonicity； gamma function； digamma function； trigamma function； logarithmic derivative； linear combination； inequality；
【Key words】 Bernoulli number； ratio； generating function； complete monotonicity； gamma function； digamma function； trigamma function； logarithmic derivative； linear combination； inequality；
【基金】 partially supported by the NationalNature Science Foundation of China (12061033)
  • 【文献出处】 Acta Mathematica Scientia ,数学物理学报 , 编辑部邮箱 ,2022年02期
  • 【分类号】O174
  • 【下载频次】14
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