Approximation and inequalities for the factorial function related to the Burnside’s formula

Abstract

In this paper, we present a continued fraction approximation and some inequalities of the factorial function based on the Burnside's formula. This approximation is fast in comparison with the recently discovered asymptotic series. Finally, some numerical computations are provided for demonstrating the superiority of our approximation over the Burnside's formula and the classical Stirling's series.