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|Title:||Quadratic iterations to π associated with elliptic functions to the cubic and septic base|
|Authors:||Chan, H.H. |
|Source:||Chan, H.H., Chua, K.S., Solé, P. (2003-04). Quadratic iterations to π associated with elliptic functions to the cubic and septic base. Transactions of the American Mathematical Society 355 (4) : 1505-1520. ScholarBank@NUS Repository. https://doi.org/10.1090/S0002-9947-02-03192-6|
|Abstract:||In this paper, properties of the functions Ad(q), Bd(q) and Cd(q) are derived. Specializing at d = 1 and 2, we construct two new quadratic iterations to π. These are analogues of previous iterations discovered by the Borweins (1987), J. M. Borwein and F. G. Garvan (1997), and H. H. Chan (2002). Two new transformations of the hypergeometric series 2F1(l/3, 1/6; 1; z) are also derived.|
|Source Title:||Transactions of the American Mathematical Society|
|Appears in Collections:||Staff Publications|
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