A probabilistic proof of Wallis's formula for pi

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.

Ver 1.1, 7 pages (slightly condensed version will appear in the Notes section of the American Mathematical Monthly)

References in corpus (1)

• Irrationality measure and lower bounds for pi(x)

Cited by in corpus (1)

• Quantum Mechanical Derivation of the Wallis Formula for $\pi$