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A new Stirling series as continued fraction

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Valahia University of Târgovişte, Bd. Unirii 18, 130082, Târgovişte, Romania

    Cristinel Mortici

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  1. Cristinel Mortici
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Correspondence to Cristinel Mortici.

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Mortici, C. A new Stirling series as continued fraction. Numer Algor 56, 17–26 (2011). https://doi.org/10.1007/s11075-010-9370-4

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