On Ramanujan’s continued fractions of order twenty-four

Abstract

Two continued fractions U(q) and V(q) of order twenty-four are obtained from a general continued fraction identity of Ramanujan. Some theta-function and modular identities for U(q) and V(q) are established to prove general theorems for the explicit evaluations of U(±q) and V(±q). From the theta-function identities of U(q) and V(q), three colour partition identities are derived as application to partition theory of integer. Further, 2-, 4- and 8-dissection formulas are established for the continued fractions U∗(q)≔q−5/2U(q) and V∗(q)≔q−1/2V(q), and their reciprocals.