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A One-Sentence and Truly Elementary Proof of the Basel Problem

2015/02/06 by Samuel G. Moreno, Moreno, Samuel G. · 1 citation
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #History and Overview (math.HO) #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1502.07667

openalex publication_date 2015/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By doing a slight change to a beautiful and widely unknown argument by E. L. Stark [E. L. Stark, Application of a Mean Value Theorem for Integrals to Series Summation, Amer. Math. Monthly 85 (1978) 481--483.] we get a candidate to be considered as one of the shortest and most elementary proofs of the celebrated Basel Problem. Furthermore, we give a comprehensive list of references on this topic, displayed in chronological order from Euler to present.

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