Two great theorems of Lord Brouncker and his formula \(b(s-1)b(s+1) = s^2\), \(b(s)= s + { \frac{1^2}{2s+{\frac{3^2}{2s + {\frac{5^2}{2s+{}_{\ddots}}}}}} }\)

DOI10.1007/s00283-010-9155-6zbMath1215.11001OpenAlexW2009580116MaRDI QIDQ2430544

Sergey Khrushchev

Publication date: 7 April 2011

Published in: The Mathematical Intelligencer (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00283-010-9155-6

zbMATH Keywords

continued fractions

Mathematics Subject Classification ID

History of number theory (11-03) Continued fractions (11A55) History of mathematics in the 17th century (01A45) Convergence and divergence of continued fractions (40A15)

Related Items (2)

Generalized Brouncker's continued fractions and their logarithmic derivatives ⋮ Euler’s reflection formula, infinite product formulas, and the correspondence principle of quantum mechanics

Cites Work

• Wallis's product, Brouncker's continued fraction, and Leibniz's series
• A recovery of Brouncker's proof for the quadrature continued fraction
• Pianos and Continued Fractions
• Archimedes' Cattle Problem
• Catching Proteus: the collaborations of Wallis and Brounker. I. Squaring the circle
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