A recovery of Brouncker's proof for the quadrature continued fraction

DOI10.5565/PUBLMAT_50106_01zbMath1128.30007OpenAlexW2133492440MaRDI QIDQ2458364

Sergey Khrushchev

Publication date: 31 October 2007

Published in: Publicacions Matemàtiques (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/41580

zbMATH Keywords

orthogonal polynomialsspecial functionscontinued fractioninfinite products

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Continued fractions (11A55) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Continued fractions; complex-analytic aspects (30B70) Other special orthogonal polynomials and functions (33C47) History of mathematics in the 17th century (01A45)

Related Items (6)

Morphing Lord Brouncker's continued fraction for π into the product of Wallis ⋮ Wallis type formula and a few versions of the number \(\pi\) in \(q\)-calculus ⋮ Two great theorems of Lord Brouncker and his formula \(b(s-1)b(s+1) = s^2\), \(b(s)= s + { \frac{1^2}{2s+{\frac{3^2}{2s + {\frac{5^2}{2s+{}_{\ddots}}}}}} }\) ⋮ Lord Brouncker's forgotten sequence of continued fractions for pi ⋮ Unnamed Item ⋮ On application of Euler's differential method to a continued fraction depending on parameter

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