Numerical Algorithms

, Volume 56, Issue 1, pp 17–26 | Cite as

A new Stirling series as continued fraction

Original Paper


We introduce the following new Stirling series
$$ n!\sim \sqrt{2\pi n}\left( \frac{n}{e}\right) ^{n}\exp \frac{1}{12n+\frac{ \frac{2}{5}}{n+\frac{\frac{53}{210}}{n+\frac{\frac{195}{371}}{n+\frac{\frac{ 22,\!999}{22,\!737}}{n+\ddots}}}}}, $$
as a continued fraction, which is faster than the classical Stirling series.


Stirling formula Rate of convergence Approximations Asymptotic expansions 

Mathematics Subject Classifications (2000)

33B15 41A10 42A16 


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Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  1. 1.Department of MathematicsValahia University of TârgovişteTârgovişteRomania

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