# A Probabilistic Proof of a Wallis-type Formula for the Gamma Function

## TL;DR

This paper employs probabilistic limit theorems to derive a Wallis-type product formula for the gamma function, offering a new probabilistic proof of classical formulas for pi and the gamma function's duplication formula.

## Contribution

It introduces a novel probabilistic approach to deriving Wallis-type formulas for the gamma function, connecting probability theory with special function identities.

## Key findings

- Probabilistic proof of Wallis's product for pi
- Derivation of the gamma function duplication formula
- New connections between probability theory and special functions

## Abstract

We use well-known limit theorems in probability theory to derive a Wallis-type product formula for the gamma function. Our result immediately provides a probabilistic proof of Wallis's product formula for $\pi$, as well as the duplication formula for the gamma function.