Theta-function identitiesof Ramanujan's continued fractions of order fourteen and twenty-eight, partition identities and vanishing coefficients

We obtain q-continued fractions S₁(q), S₂(q) and S₃(q) of order fourteen, and continued fractions V₁(q), V₂(q) and V₃(q) of order twenty-eight as special cases of a general continued fraction identity of Ramanujan. We prove some theta-function identities for the continued fractions and show that colour partition identities can be deduced from the theta-function identities. Some vanishing coefficients results arising from the continued fractions are also offered.