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International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 40, Pages 2149-2159
http://dx.doi.org/10.1155/S0161171204111058

Some theorems on the explicit evaluation of Ramanujan's theta-functions

Department of Mathematical Sciences, Tezpur University, Napaam 784 028, Sonitpur, Assam, India

Received 8 October 2001

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Bruce C. Berndt et al. and Soon-Yi Kang 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.