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

Adiga, Chandrashekar and Kim, T. and Naika, M. S. M. and Madhusudhan, H. S. (2004) On Ramanujan's cubic continued fraction and explicit evaluations of theta-functions. Indian Journal of Pure and Applied Mathematics, 35 (9). pp. 1047-1062. ISSN 0019-5588

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Abstract

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.

Item Type: Article
Uncontrolled Keywords: cubic continued fraction; integral representation; modular equation; theta-function; transformation formula
Subjects: E Mathematical Science > Mathematics
Divisions: Department of > Mathematics
Depositing User: Users 23 not found.
Date Deposited: 03 Sep 2019 11:26
Last Modified: 08 Jul 2022 11:15
URI: http://eprints.uni-mysore.ac.in/id/eprint/6550

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