Zagier provided eleven conjectural rank two examples for Nahm's problem. All of them have been proved in the literature except for the fifth example, and there is no q-series proof for the tenth example. We prove that the fifth and the tenth examples are in fact equivalent. Then we give a q-series proof for the fifth example, which confirms a recent conjecture of Wang. This also serves as the first q-series proof for the tenth example, whose explicit form was conjectured by Vlasenko and Zwegers in 2011 and whose modularity was proved by Cherednik and Feigin in 2013 via nilpotent double affine Hecke algebras.

中文翻译：

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关于 Zagier 的一些双 Nahm 和

扎吉尔为纳姆的问题提供了十一个推测性的二级例子。除了第五个例子外，所有这些都在文献中得到了证明，第十个例子没有q级数证明。我们证明第五个和第十个例子实际上是等价的。然后我们给出第五个例子的q级证明，这证实了Wang最近的猜想。这也是第十个例子的第一个q级数证明，其显式形式由 Vlasenko 和 Zwegers 在 2011 年猜想，其模块化性由 Cherednik 和 Feigin 在 2013 年通过幂零双仿射 Hecke 代数证明。