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Published online by Cambridge University Press: 03 November 2016
In the following note, Stirling’s formula for a factorial is first found by a very simple process. The expression so obtained has a meaning for non-integral as well as integral values of the variable. The function it defines is easily seen (§§ 3 ff.) to possess the fundamental properties of the Gamma function, and provides an easy and natural avenue of approach to its study.
page no 115 note * In the same way we get, by taking the next term in the logarithmic series,
and if we note that
we find 
It is easy to get another term or two of the asymptotic fieries in this way, with the appropriate inequality.
page no 118 note *
It follows that the conditiorl 
is satisfied if 
page no 119 note † If we use the lemmas
we get easily enough
page no 119 note ‡
page no 120 note * Cf. the results given by Lindelöf, , Calcul des Rksidus (Paris, 1905), Ch. IV.Google Scholar