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

Xu You

doi:10.56754/0719-0646.2602.317

DOI:

https://doi.org/10.56754/0719-0646.2602.317

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.

Keywords

Factorial function , Stirling’s formula , Burnside’s formula , approximation , continued fraction

Mathematics Subject Classification:

11Y60 , 11A55 , 41A25

Xu You Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology, Beijing 102617, P. R. China. https://orcid.org/0000-0003-2591-5365

Pages: 317–326
Date Published: 2024-08-08
Vol. 26 No. 2 (2024)

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