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Logarithmic convexity and increasing property of the Bernoulli numbers and their ratios

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In the paper, with the aid of the Čebyšev integral inequality, by virtue of the integral representation of the Riemann zeta function, with the use of two properties of a function and its derivatives involving the exponential function and the Stirling numbers of the second kind, by means of complete monotonicity, the authors establish logarithmic convexity and increasing property of four sequences involving the Bernoulli numbers and their ratios.

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Acknowledgements

The authors appreciate anonymous referees for their careful corrections to and valuable comments on the original version of this paper.

Funding

The first author, Mrs. Ye Shuang, was partially supported by the National Natural Science Foundation of China (Grant No. 11901322), by the Natural Science Foundation of Inner Mongolia (Grant No. 2018LH01002), and by the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region (Grant No. NJZY19157), China.

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Authors and Affiliations

  1. College of Mathematics and Physics, Inner Mongolia University for Nationalities, Tongliao, 028043, Inner Mongolia, China

    Ye Shuang

  2. School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, 454010, Henan, China

    Bai-Ni Guo

  3. School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin, 300387, China

    Feng Qi

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  1. Ye Shuang
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  2. Bai-Ni Guo
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  3. Feng Qi
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Correspondence to Bai-Ni Guo or Feng Qi.

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Dedicated to Dr. Professor Sever Silvestru Dragomir at Victoria University in Australia.

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Shuang, Y., Guo, BN. & Qi, F. Logarithmic convexity and increasing property of the Bernoulli numbers and their ratios. RACSAM 115, 135 (2021). https://doi.org/10.1007/s13398-021-01071-x

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