A probabilistic proof of Wallis's formula for pi

TL;DR

This paper provides a probabilistic proof of Wallis's formula for pi, utilizing elementary probability functions, normalization constants, and special functions like the Gamma function, the standard normal, and Student t-distribution.

Contribution

It introduces a novel probabilistic approach to prove Wallis's formula, connecting elementary probability with special functions and classical mathematical constants.

Findings

Probabilistic proof of Wallis's formula for pi.

Connection between probability distributions and classical constants.

Use of elementary probability and special functions in proof.

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.