International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 40, Pages 2149-2159
doi: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 Nayandeep Deka Baruah and P. Bhattacharyya. 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.