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The American Mathematical Monthly Volume 127, 2020 - Issue 1
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Notes

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

Wooyoung ChinDepartment of Mathematical Sciences, KAIST, Daejeon34141, Republic of KoreaCorrespondence[email protected]
ORCID Iconhttp://orcid.org/0000-0003-3960-4103
ORCID Icon
Pages 75-79 | Received 08 Aug 2018, Accepted 16 Jul 2019, Published online: 19 Dec 2019
 
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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.

Acknowledgments

The author would like to thank the reviewers for several valuable comments and references. He would also like to thank his friends Kihyun Kim and Taehyun Eom for helpful suggestions.

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