Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-02-06T01:08:00.843Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on Stirling's Theorem

Published online by Cambridge University Press:  31 October 2008

J. R. Wilton
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 28 , January 1933 , pp. xii - xiii
Copyright
Copyright © Edinburgh Mathematical Society 1933