On Ramanujan's cubic continued fraction and explicit evaluations of theta-functions

By Chandrashekar Adiga, Kim Taekyun, M. Naika, H. S. Madhusudhan. 2004

61 citations recorded by the source corpus.

In this paper we give two integral representations for the Ramanuian's cubic continued fraction V(q) and also derive a modular equation relating V(q) and V(q(3)). We also establish some modular equations and a transformation formula for Ramanujan's theta-function psi(-q). As an application of these, we compute several new explicit evaluations of theta-functions and Ramanujan's cubic continued fraction.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/082458453ac41c7b21238d3d4a3f75c8193be9aa

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Heng Huat Chan
2. Nayandeep Deka Baruah
3. Kanan Kumari Ojah
4. Wadim Zudilin

In Discrete Mathematics and Combinatorics

1. Heng Huat Chan
2. Wadim Zudilin

Citations in the corpus

• RAMANUJAN'S CUBIC CONTINUED FRACTION AND RAMANUJAN TYPE CONGRUENCES FOR A CERTAIN PARTITION FUNCTION (2010, background): “For some wonderful subsequent works on the cubic continued fraction, see [1, 10, 11, 12, 15, 16, 18, 21, 32].”