New theta-function identities and general theorems for the explicit evaluations of Ramanujan’s continued fractions

Abstract

We prove some new theta-function identities for two continued fractions of Ramanujan which are analogous to those of Ramanujan-Göllnitz-Gordon continued fraction. Then these identities are used to prove new general theorems for the explicit evaluations of the continued fractions.Mathematics Subject Classification 30B70 · 33D15 · 33D90 · 11F20