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Research Article Open Access

Elementary Combinatorial-Probabilistic Proof of the Wallis and Stirling Formulas

Mikhail Kovalyov

Abstract

This short note provides a remarkably simple derivation of the Wallis and Stirling formulas based on elementary estimates applied to binomial coefficients. As a byproduct an elementary proof of the central limit theorem for the binomial distribution is also obtained.

Journal of Mathematics and Statistics
Volume 5 No. 4, 2009, 408-410

DOI: https://doi.org/10.3844/jmssp.2009.408.410

Submitted On: 26 June 2009 Published On: 31 December 2009

How to Cite: Kovalyov, M. (2009). Elementary Combinatorial-Probabilistic Proof of the Wallis and Stirling Formulas. Journal of Mathematics and Statistics, 5(4), 408-410. https://doi.org/10.3844/jmssp.2009.408.410

Open AccessCopyright: © 2009 Mikhail Kovalyov. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Wallis formula
  • Stirling formula
  • normal distribution