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.