AI 中文总结
该研究借助拉马努金连分数恒等式推导偶数阶广义连分数，建立theta函数恒等式，以76阶连分数为例得到分拆理论恒等式等，推广了拉马努金连分数。
AI 中文摘要
本文借助拉马努金的一个一般连分数恒等式，推导出任意偶数阶\(k\)的三个广义连分数，并为这些连分数建立了一般theta函数恒等式。作为76阶连分数的应用，我们得到了分拆理论恒等式和一些系数消失结果。
英文摘要
In this paper, we derive three generalized continued fractions of any even order $k$ with the aid of a general continued fraction identity of Ramanujan and we establish general theta function identities for these continued fractions. As an application of continued fraction of order seventy-six, we obtain partition theoretic identities and some vanishing coefficient results.
