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The Ramanujan Journal

, Volume 46, Issue 1, pp 119–125 | Cite as

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

  • Dawei Lu
  • Xiaoguang Wang
  • Lixin Song
  • Huiyuan Xu
Article

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.

Keywords

Continued fraction Approximation Rate of convergence Inequalities Gamma function 

Mathematics Subject Classification

11J70 33B15 41A25 26D15 41A10 

Notes

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.

References

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    Mortici, C., Qi, F.: Asymptotic formulas and inequalities for the Gamma function in terms of the Tri-gamma function. Results Math. 67, 395–402 (2015)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Dawei Lu
    • 1
    • 2
  • Xiaoguang Wang
    • 1
  • Lixin Song
    • 1
  • Huiyuan Xu
    • 1
  1. 1.School of Mathematical SciencesDalian University of TechnologyDalianChina
  2. 2.Department of StatisticsThe Chinese University of Hong KongShatin, N.T.Hong Kong

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