Elementary Combinatorial-Probabilistic Proof of the Wallis and Stirling Formulas | Science Publications

Journal of Mathematics and Statistics

Elementary Combinatorial-Probabilistic Proof of the Wallis and Stirling Formulas

Mikhail Kovalyov

DOI : 10.3844/jmssp.2009.408.410

Journal of Mathematics and Statistics

Volume 5, Issue 4

Pages 408-410

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.

Copyright

© 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.