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

2019/07/28 by Wooyoung Chin, Chin, Wooyoung
Mathematics · #11Y60 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1907.12095

openalex publication_date 2019/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 π, as well as the duplication formula for the gamma function.

Related

• Generalising the Wallis Product
• Wallis's Formula and the Probability Integral
• Generalizing Wallis formula
• Euler and the Duplication Formula for the Gamma-Function
• From e to π: Derivation of the Wallis formula for π from e