On Ramanujan’s continued fractions of order twenty-four

Abstract

Two continued fractions $U\left(q\right)$ and $V\left(q\right)$ of order twenty-four are obtained from a general continued fraction identity of Ramanujan. Some theta-function and modular identities for $U\left(q\right)$ and $V\left(q\right)$ are established to prove general theorems for the explicit evaluations of $U(\pm q)$ and $V(\pm q)$. From the theta-function identities of $U\left(q\right)$ and $V\left(q\right)$, 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 $U^{\ast }\left(q\right)≔q^{-5/2}U\left(q\right)$ and $V^{\ast }\left(q\right)≔q^{-1/2}V\left(q\right)$, and their reciprocals.