Transactions of the American Mathematical Society

Quadratic iterations to ${\pi}$ associated with elliptic functions to the cubic and septic base

Author(s): Heng Huat Chan; Kok Seng Chua; Patrick Solé
Journal: Trans. Amer. Math. Soc. 355 (2003), 1505-1520.
MSC (2000): Primary 11Y60, 33C05, 33E05, 11F03
Posted: December 2, 2002
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Abstract: In this paper, properties of the functions

and

are derived. Specializing at

and

, we construct two new quadratic iterations to $\pi$ . 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

are also derived.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 11Y60, 33C05, 33E05, 11F03

Heng Huat Chan
Affiliation: Department of Mathematics, National University of Singapore, Singapore 117543, Republic of Singapore
Email: chanhh@math.nus.edu.sg

Kok Seng Chua
Affiliation: Department of Mathematics, National University of Singapore, Singapore 117543, Republic of Singapore
Email: matv2@nus.edu.sg

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