Some theorems on the explicit evaluation of Ramanujan's theta-functions
type: Item
instance of: scholarly article
title: Some theorems on the explicit evaluation of Ramanujan's theta-functions
zbMATH Open document ID: 1155.11324
DOI: 10.1155/S0161171204111058
author: Niranjan Chakravarthy
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-25T00:00:00Z
full work available at URL: https://eudml.org/doc/55061
review text: Summary: \textit{Bruce C. Berndt} et al. [with \textit{H. H. Chan}, Mathematika 42, No. 2, 278--294 (1995; Zbl 0862.33016), with Chan and \textit{L.-C. Zhang}, Acta Arith. 73, No. 1, 67--85 (1995; Zbl 0843.11007)] and \textit{Soon-Yi Kang} [Acta Arith. 90, No. 1, 49--68 (1999; Zbl 0933.11003), Ramanujan J. 3, No. 1, 91--111 (1999; Zbl 0930.11025)] have proved many of Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions in terms of Weber-Ramanujan class invariants. In this note, we give alternative proofs of some of these identities of theta-functions recorded by Ramanujan in his notebooks and deduce some formulas for the explicit evaluation of his theta-functions in terms of Weber-Ramanujan class invariants.
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 11F20
zbMATH DE Number: 2171579
zbMATH Keywords: explicit evaluation
zbMATH Keywords: Rogers-Ramanujan continued fraction
zbMATH Keywords: theta-functions
zbMATH Keywords: Weber-Ramanujan class invariants
zbMATH Keywords: alternative proofs of identities of Ramanujan's theta-functions
MaRDI profile type: Publication
OpenAlex ID: W2123424468
description: scientific article; zbMATH DE number 2171579