On a New Stirling’s Series

Abstract

In this paper, we deduced the following new Stirling series:

\[ n! \sim \sqrt{2n\pi} (\frac{n}{2})^n exp(\frac{1}{12n+1}[1 + \frac{1}{12n} (1+\frac{\frac{2}{5}}{n} + \frac{\frac{29}{150}}{n^2} – \frac{\frac{62}{2625}}{n^3} – \frac{\frac{9173}{157500}}{n^4} +\ldots )^{-1}]) ,\]

which is faster than the classical Stirling’s series.