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Some properties of the psi function and evaluations of γ

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Abstract

In this paper, the authors show some monotonicity and concavity of the classical psi function, by which several known results are improved and some new asymptotically sharp estimates are obtained for this function. In addition, applying the new results to the psi function, the authors improve the well-known lower and upper bounds for the approximate evaluation of Euler’s constant γ.

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Authors and Affiliations

  1. School of Science, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Song-liang Qiu & Xue Zhao

Authors
  1. Song-liang Qiu
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  2. Xue Zhao
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Corresponding author

Correspondence to Song-liang Qiu.

Additional information

Supported by the National Natural Science Foundation of China (11171307).

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Qiu, Sl., Zhao, X. Some properties of the psi function and evaluations of γ. Appl. Math. J. Chin. Univ. 31, 103–111 (2016). https://doi.org/10.1007/s11766-016-3272-8

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  • DOI: https://doi.org/10.1007/s11766-016-3272-8

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