Per citar aquest document:
A recovery of Brouncker's proof for the quadrature continued fraction
Khrushchev, Sergey (Atilim University (Ankara, Turquia). Department of Mathematics)

Data: 2006
Resum: 350 years ago in Spring of 1655 Sir William Brouncker on a request by John Wallis obtained a beautiful continued fraction for 4/π. Brouncker never published his proof. Many sources on the history of Mathematics claim that this proof was lost forever. In this paper we recover the original proof from Wallis’ remarks presented in his “Arithmetica Infinitorum”. We show that Brouncker’s and Wallis’ formulas can be extended to MacLaurin’s sinusoidal spirals via related Euler’s products. We derive Ramanujan’s formula from Euler’s formula and, by using it, then show that numerators of convergents of Brouncker’s continued fractions coincide up to a rotation with Wilson’s orthogonal polynomials corresponding to the parameters a = 0, b = 1/2, c = d = 1/4.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Publicat a: Publicacions Matemàtiques, V. 50 n. 1 (2006) p. 3-42, ISSN 0214-1493

Adreça original:
DOI: 10.5565/PUBLMAT_50106_01
DOI: 10.5565/34548

40 p, 307.2 KB

El registre apareix a les col·leccions:
Articles > Articles publicats > Publicacions matemàtiques
Articles > Articles de recerca

 Registre creat el 2006-05-09, darrera modificació el 2017-05-18

   Favorit i Compartir