Original proofs of Stirling's series for log(n!)

2017/01/24 by Jacques Gélinas, Gélinas, Jacques
Mathematics · #11B68 #34A05 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics

paper · pdf · doi:10.48550/arxiv.1701.06689

openalex publication_date 2017/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Transcription into modern notations of the derivation by Stirling and De Moivre of an asymptotic series for log(n!), usually called Stirling's series. The previous discovery by Wallis of an infinite product for π, and later results on the divergence of the series are also presented. We conclude that James Stirling has priority over Abraham de Moivre for Stirling's formula and Stirling's series.

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