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

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Keywords

  • Wallis formula
  • Stirling formula
  • normal distribution