# Ramanujan's cubic continued fraction revisited

@article{Chan2007RamanujansCC, title={Ramanujan's cubic continued fraction revisited}, author={Heng Huat Chan and Kok Loo}, journal={Acta Arithmetica}, year={2007}, volume={126}, pages={305-313} }

In this article, we derive a sequence of numbers which converge to 1/π. We will also derive a new series for 1/π. These new results are motivated by the study of Ramanujan’s cubic continued fraction.

#### 13 Citations

A new proof of two identities involving Ramanujan’s cubic continued fraction

- Mathematics
- 2010

In this paper, we give a new proof of two identities involving Ramanujan’s cubic continued fraction. These identities are the key ingredients to an analog of Ramanujan’s “Most Beautiful Identity”… Expand

The Rogers-Ramanujan continued fraction and a quintic iteration for 1/

- Mathematics
- 2007

Properties of the Rogers-Ramanujan continued fraction are used to obtain a formula for calculating 1/π with quintic convergence.

Rational analogues of Ramanujan's series for 1/π†

- Mathematics
- Mathematical Proceedings of the Cambridge Philosophical Society
- 2012

Abstract A general theorem is stated that unifies 93 rational Ramanujan-type series for 1/π, 40 of which are believed to be new. Moreover, each series is shown to have a companion identity, thereby… Expand

RAMANUJAN'S CUBIC CONTINUED FRACTION AND AN ANALOG OF HIS "MOST BEAUTIFUL IDENTITY"

- Mathematics
- 2010

In this paper, we prove an analog of Ramanujan's "Most Beautiful Identity". This analog is closely related to Ramanujan's beautiful results involving the cubic continued fraction.

Eisenstein series and Ramanujan-type series for 1/π

- Mathematics
- 2010

Using certain representations for Eisenstein series, we uniformly derive several Ramanujan-type series for 1/π.

RAMANUJAN'S CUBIC CONTINUED FRACTION AND RAMANUJAN TYPE CONGRUENCES FOR A CERTAIN PARTITION FUNCTION

- Mathematics
- 2010

In this paper, we study the divisibility of the function a(n) defined by $\sum_{n\geq 0} a(n) q^n := (q;q)^{-1}_\infty (q^2; q^2)^{-1}_\infty $. In particular, we prove certain "Ramanujan type cong...

A summation formula and Ramanujan type series

- Mathematics
- 2012

Abstract Using some properties of the general rising shifted factorial and the gamma function we derive a variant form of Dougallʼs F 4 5 summation for the classical hypergeometric functions. This… Expand

Ramanujan’s series for 1/π: A survey (2009)

- Mathematics
- 2016

Paper 19: Nayandeep Deka Baruah, Bruce C. Berndt and Heng Huat Chan, “Ramanujan’s series for 1/π: A survey,” American Mathematical Monthly, vol. 116 (2009), p. 567–587. Copyright 2009 Mathematical… Expand

Sporadic sequences, modular forms and new series for 1/π

- Mathematics
- 2012

Two new sequences, which are analogues of six sporadic examples of D. Zagier, are presented. The connection with modular forms is established and some new series for 1/π are deduced. The experimental… Expand

New analogues of Clausen’s identities arising from the theory of modular forms | NOVA. The University of Newcastle's Digital Repository

- Mathematics, Engineering
- 2011

Abstract Around 1828, T. Clausen discovered that the square of certain hypergeometric F 1 2 function can be expressed as a hypergeometric F 2 3 function. Special cases of Clausenʼs identities were… Expand

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