  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 $\pi$, 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.
