Recently, 4-regular partitions into distinct parts were connected with a family of overpartitions. In this paper, we provide a uniform extension of two relations due to Andrews for the two types of partitions. Such an extension is made possible with recourse to a new trivariate Rogers–Ramanujan type identity, which concerns a family of quadruple summations appearing as generating functions for the aforementioned overpartitions. More interestingly, the derivation of this Rogers–Ramanujan type identity is relevant to a certain well-poised basic hypergeometric series.

中文翻译：

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链接分区理想和四元求和族

最近，分成不同部分的 4-正则分区与一系列超分区相关联。在本文中，我们为两种类型的分区提供了安德鲁斯两种关系的统一扩展。这种扩展可以通过求助于新的三变量罗杰斯-拉马努金型恒等式来实现，该恒等式涉及作为上述过度划分的生成函数出现的四重求和族。更有趣的是，这种罗杰斯-拉马努金型恒等式的推导与某种平衡良好的基本超几何级数有关。