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.

中文翻译：

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关于拉马努金的二十四阶连分数

两个连分数$U（q）$和$V（q）$二十四阶是从拉马努金的一般连分式恒等式中获得的。一些 theta 函数和模块化恒等式$U（q）$和$V（q）$建立来证明显式评估的一般定理$U（\pm q）$和$V（\pm q）$。从 theta 函数恒等式$U（q）$和$V（q）$，导出了三个颜色分区恒等式作为整数分区理论的应用。更远，$2$-,$4$- 和$8$- 建立连分数的剖分公式$U^{*}（q）≔q^{-5/2}U（q）$和$V^{*}（q）≔q^{-1/2}V（q）$，以及它们的倒数。