A continued fraction expansion for a -tangent function.
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Fulmek, Markus (2000)
Séminaire Lotharingien de Combinatoire [electronic only]
Prodinger, Helmut (2008)
Séminaire Lotharingien de Combinatoire [electronic only]
M. Mahadeva Naika, B. Dharmendra, K. Shivashankara (2008)
Open Mathematics
In this paper, we establish several explicit evaluations, reciprocity theorems and integral representations for a continued fraction of order twelve which are analogues to Rogers-Ramanujan’s continued fraction and Ramanujan’s cubic continued fraction.
Zongduo Dai, Ping Wang, Kunpeng Wang, Xiutao Feng (2007)
Acta Arithmetica
Hiroshi Ito (2004)
Acta Arithmetica
Norman Richert (1990)
Acta Arithmetica
Edward B. Burger, David C. Clyde, Cory H. Colbert, Gea Hyun Shin, Zhaoning Wang (2012)
Acta Arithmetica
Kopetzky, Hans Günther, Schnitzer, Franz Josef (1995)
Mathematica Pannonica
A. Rockett, P. Szüsz (1986)
Acta Arithmetica
Cor Kraaikamp (1991)
Acta Arithmetica
Velibor Bojković, Jovana Nikolić, Mladen Zekić (2023)
Czechoslovak Mathematical Journal
It is clear that every rational surgery on a Hopf link in -sphere is a lens space surgery. In this note we give an explicit computation which lens space is a resulting manifold. The main tool we use is the calculus of continued fractions. As a corollary, we recover the (well-known) result on the criterion for when rational surgery on a Hopf link gives the -sphere.
Mollin, R.A. (2005)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
Komatsu, Takao (2007)
Integers
Sergey Khrushchev (2006)
Publicacions Matemàtiques
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...
Weiqun Hu (2000)
Acta Arithmetica
Mollin, R.A. (2001)
The New York Journal of Mathematics [electronic only]
Johannes Buchmann (1985)
Journal für die reine und angewandte Mathematik
E. Heine, C.G.J. Jacobi (1868)
Journal für die reine und angewandte Mathematik
J. Allouche, M. Mendès France, A. van der Poorten (1991)
Acta Arithmetica
J. Hermes (1894)
Mathematische Annalen
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