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A Note on Stirling's Theorem
Published online by Cambridge University Press: 31 October 2008
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Let Γ(1 + x) = √(2πx)xxe–x φ(x);
This result is Stirling's theorem. A simple proof is given in § 1.87 of Titchmarsh's Theory of Functions (Oxford Univ. Press, 1932).
Rather more than Stirling's theorem can be proved by a method which assumes nothing but the definition of the Γ-function, and Γ (½) = √π, from which it follows that
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- Copyright © Edinburgh Mathematical Society 1933
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