A Proof of (2)=²/6 Involving a Fourier-Legendre Expansion

AMERICAN MATHEMATICAL MONTHLY（2024）

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摘要

We give a new proof of Euler's famous formula zeta (2)=pi 2/6 using a 1954 result by M. O. Gonzalez which expands the complete elliptic integral of the first kind in terms of Legendre polynomials.

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A Proof of (2)=2/6 Involving a Fourier-Legendre Expansion

A Proof of (2)=²/6 Involving a Fourier-Legendre Expansion