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A new sharp approximation for the Gamma function related to Burnside’s formula

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Abstract

In this paper, based on Burnside’s formula, a similar continued fraction approximation of the factorial function and some inequalities for the gamma function are established. Finally, for demonstrating the superiority of our new series over the Burnside’s formula and the classical Stirling’s series, some numerical computations are given.

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Notes

  1. See http://www.rskey.org/gamma.htm.

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Authors and Affiliations

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

    Dawei Lu

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  1. Dawei Lu
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Correspondence to Dawei Lu.

Additional information

The research of the author is Supported by the National Natural Sciences Foundation of China (grant number 11101061 and 11371077), Research Foundation for Doctor of Liaoning Province (grant number 20121016) and the Fundamental Research Funds for the Central Universities (grant number DUT12LK16 and DUT13JS06).

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Lu, D. A new sharp approximation for the Gamma function related to Burnside’s formula. Ramanujan J 35, 121–129 (2014). https://doi.org/10.1007/s11139-013-9534-7

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  • DOI: https://doi.org/10.1007/s11139-013-9534-7

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