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Complete monotonicity of a function involving the divided difference of digamma functions

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Abstract

In the paper, necessary and sufficient conditions are provided for a function involving the divided difference of two psi functions to be completely monotonic. Consequently, a class of inequalities for sums are presented, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions are derived, and two double inequalities for bounding the ratio of two gamma functions are discovered.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454010, China

    Feng Qi & BaiNi Guo

  2. Department of Mathematics, Chongqing Normal University, Chongqing, 401331, China

    QiuMing Luo

Authors
  1. Feng Qi
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  2. QiuMing Luo
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  3. BaiNi Guo
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Correspondence to Feng Qi.

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Qi, F., Luo, Q. & Guo, B. Complete monotonicity of a function involving the divided difference of digamma functions. Sci. China Math. 56, 2315–2325 (2013). https://doi.org/10.1007/s11425-012-4562-0

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  • DOI: https://doi.org/10.1007/s11425-012-4562-0

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