Explicit Values and Vanishing Coefficients for Ramanujan's Continued Fractions of Order Twenty with Applications

Abstract

Two $q$-continued fractions of order twenty are obtained from a general continued fraction identity of Ramanujan. Some theta-function identities are established for the two continued fractions and are used to prove general theorems for the explicit evaluation of the continued fractions. Some partition theoretic results and vanishing coefficient  arising from $q$-products of the continued fractions are also offered.