A probabilistic proof of Wallis's formula for pi
Number Theory
2010-11-16 v2 Probability
Abstract
Using mostly elementary results and functions from probability, we prove Wallis's formula for pi: pi/2 = prod_n (2n * 2n) / ((2n-1) * (2n+1)). The proof involves normalization constants and the Gamma function, Standard normal, and the Student t-Distribution.
Keywords
Cite
@article{arxiv.0709.2181,
title = {A probabilistic proof of Wallis's formula for pi},
author = {Steven J. Miller},
journal= {arXiv preprint arXiv:0709.2181},
year = {2010}
}
Comments
Ver 1.1, 7 pages (slightly condensed version will appear in the Notes section of the American Mathematical Monthly)