Abstract
In this paper, based on the Burnside’s formula, some accurate approximation and double inequality for the gamma function are established. Finally, for demonstrating the superiority of our new series over the Burnside’s formula and other classical or recently discovered asymptotic series, some numerical computations are provided.
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Acknowledgments
Part of the research was done in the Department of Statistics, the Chinese University of Hong Kong. The first author thanks Professor Qi-Man Shao and the staff for their hospitality and for providing excellent academic and living environments.
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The first author was supported by the National Natural Science Foundation of China (Grant Nos. 11371077 and 11571058), the Fundamental Research Funds for the Central Universities (Grant No. DUT15LK19) and Hong Kong RGC GRF (Grant No. 14302515).
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Lu, D., Liu, X. & Qu, T. Continued fraction approximations and inequalities for the gamma function by Burnside. Ramanujan J 42, 491–500 (2017). https://doi.org/10.1007/s11139-016-9876-z
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DOI: https://doi.org/10.1007/s11139-016-9876-z