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A ratio of finitely many gamma functions and its properties with applications

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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, the authors establish an inequality involving exponential functions and sums, introduce a ratio of finitely many gamma functions, discuss properties, including monotonicity, logarithmic convexity, (logarithmically) complete monotonicity, and the Bernstein function property, of the newly introduced ratio, and construct two inequalities of multinomial coefficients and multivariate beta functions.

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Acknowledgements

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

Author information

Authors and Affiliations

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

    Feng Qi & Shu-Bin Yu

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

    Feng Qi

  3. Department of Fundamental Courses, Zhengzhou University of Science and Technology, Zhengzhou, 450064, Henan, China

    Wen-Hui Li

  4. School of Computer Science and Technology, Tianjin Polytechnic University, Tianjin, 300387, China

    Xin-Yu Du

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

    Bai-Ni Guo

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  1. Feng Qi
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  2. Wen-Hui Li
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  4. Xin-Yu Du
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Correspondence to Bai-Ni Guo.

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In memory of the first author’s mother, Ji-Rong Zhang, who passed away in December 1995.

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Qi, F., Li, WH., Yu, SB. et al. A ratio of finitely many gamma functions and its properties with applications. RACSAM 115, 39 (2021). https://doi.org/10.1007/s13398-020-00988-z

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