New identities for Ramanujan's cubic continued fraction

Abstract

In this paper, we present some new identities providing relations between Ramanujan's cubic continued fraction $V(q)$ and the other three continued fractions $V(q^9)$, $V(q^{17})$ and $V(q^{19})$. In the process, we establish some new modular equations for the ratios of Ramanujan's theta functions. We also establish some general formulas for the explicit evaluations of ratios of Ramanujan's theta functions.