A new Stirling series as continued fraction

  • Authors:
  • Cristinel Mortici

  • Affiliations:
  • Department of Mathematics, Valahia University of Târgovişte, Târgovişte, Romania 130082

  • Venue:
  • Numerical Algorithms
  • Year:
  • 2011

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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.