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Stirling's formula derived simply

2007/11/28 by Joseph B. Keller, Jean‐Marc Vanden‐Broeck, Jean-Marc Vanden-Broeck +2
Mathematics · Medicine · #11B37 #33B15 #Biomedical and Chemical Research #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:11B37 #msc:33B15

paper · pdf · doi:10.48550/arxiv.0711.4412

4 pages; omitted second author added

openalex publication_date 2007/11/28 · arxiv created 2008/05/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Stirling's formula, the asymptotic expansion of n! for n large, or of Γ(z) for z→ ∞, is derived directly from the recursion equation Γ(z+1) =z Γ(s) and the normalization condition Γ(1/2) =√π.

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