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

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- by Heng Huat Chan, Kok Seng Chua and Patrick Solé PDF
- Trans. Amer. Math. Soc.
**355**(2003), 1505-1520 Request permission

## Abstract:

In this paper, properties of the functions $A_d(q)$, $B_d(q)$ and $C_d(q)$ are derived. Specializing at $d=1$ and $2$, 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 $_2F_1(1/3,1/6;1;z)$ are also derived.## References

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## Additional Information

**Heng Huat Chan**- Affiliation: Department of Mathematics, National University of Singapore, Singapore 117543, Republic of Singapore
- MR Author ID: 365568
- 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
**Patrick Solé**- Affiliation: CNRS-I3S, ESSI, Route des Colles, 06 903 Sophia Antipolis, France
- MR Author ID: 225546
- Email: ps@essi.fr
- Received by editor(s): January 15, 2002
- Received by editor(s) in revised form: August 21, 2002
- Published electronically: December 2, 2002
- Additional Notes: The first author was funded by National University of Singapore Academic Research Fund, Project Number R14000027112
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**355**(2003), 1505-1520 - MSC (2000): Primary 11Y60, 33C05, 33E05, 11F03
- DOI: https://doi.org/10.1090/S0002-9947-02-03192-6
- MathSciNet review: 1946402