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A new continued fraction approximation and inequalities for the Gamma function via the Tri-gamma function

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Abstract

The main objective of this paper is to propose a product approximation for the Gamma function in the form of continued fraction, via the Tri-gamma function. The importance of this new formula is that the convergence of the corresponding asymptotic series is faster than other recently discovered asymptotic series, and some new inequalities related to the new formula are also established.

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Acknowledgements

Part of the research was done in the Department of Statistics, The Chinese University of Hong Kong. The first author would like to thank Professor Qi-Man Shao and the staff for their hospitality for providing excellent academic and living environments.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116023, China

    Dawei Lu, Xiaoguang Wang, Lixin Song & Huiyuan Xu

  2. Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    Dawei Lu

Authors
  1. Dawei Lu
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  2. Xiaoguang Wang
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  3. Lixin Song
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  4. Huiyuan Xu
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Corresponding author

Correspondence to Lixin Song.

Additional information

The first author is supported by the National Natural Science Foundation of China (Grant No. 11571058), the Fundamental Research Funds for the Central Universities (Grant No. DUT15LK19) and Hong Kong RGC GRF (Grant No. 14302515). The second author is supported by the National Natural Science Foundation of China (Grant No. 11471065). The second author is supported by the National Natural Science Foundation of China (Grant No. 11371077).

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Lu, D., Wang, X., Song, L. et al. A new continued fraction approximation and inequalities for the Gamma function via the Tri-gamma function. Ramanujan J 46, 119–125 (2018). https://doi.org/10.1007/s11139-016-9882-1

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  • DOI: https://doi.org/10.1007/s11139-016-9882-1

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