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Complete Monotonicity for a New Ratio of Finitely Many Gamma Functions

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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.

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Acknowledgements

The author thanks the anonymous referees for their careful corrections to, valuable comments on, and helpful suggestions regarding the original version of this paper.

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Authors and Affiliations

  1. Institute of Mathematics, Henan Polytechnic University, Jiaozuo, 454010, China

    Feng Qi  (祁锋)

  2. School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China

    Feng Qi  (祁锋)

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  1. Feng Qi  (祁锋)
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Correspondence to Feng Qi  (祁锋).

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This work was partially supported by the National Nature Science Foundation of China (12061033).

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Qi, F. Complete Monotonicity for a New Ratio of Finitely Many Gamma Functions. Acta Math Sci 42, 511–520 (2022). https://doi.org/10.1007/s10473-022-0206-9

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