Some theorems on the explicit evaluation of Ramanujan's theta-functions
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.
alternative proofs of identities of Ramanujan's theta-functions
scientific article; zbMATH DE number 2171579