International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 37-40, Pages 2149-2159
doi:10.1155/S0161171204111058

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

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.