Legendre’s Singular Modulus

DOI10.1080/00029890.2022.2094155zbMath1500.01007arXiv2002.07250OpenAlexW3006418156MaRDI QIDQ5103244

Mark B. Villarino

Publication date: 23 September 2022

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.07250

zbMATH Keywords

beta functiongamma functionthree-body problempendulumelliptic functionscubic latticeelliptic integralslemniscateLegendre's singular modulusRamanujan's elipse

Mathematics Subject Classification ID

History of mathematics in the 19th century (01A55)

Uses Software

• MathOverflow

Cites Work

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• Choreographic three bodies on the lemniscate
• Exact evaluation of the Green functions for the anisotropic face-centred and simple cubic lattices
• Braids in classical dynamics
• Lattice Sums Then and Now
• On Epstein's Zeta Function (I)
• A remarkable periodic solution of the three-body problem in the case of equal masses

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