In 2012, Andrews and Merca investigated the truncated version of the Euler pentagonal number theorem. Their work has opened up a new study on truncated theta series and has inspired several mathematicians to work on the topic. In 2019, Merca studied the Rogers-Ramanujan functions and posed three groups of conjectures on truncated series involving the Rogers-Ramanujan functions. In this paper, we present a uniform method to prove the three groups of conjectures given by Merca based on a result due to Pólya and Szegö.

中文翻译：

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Merca 在涉及 Rogers-Ramanujan 函数的截断级数上的一些猜想的证明


2012 年，Andrews 和 Merca 研究了欧拉五边形数定理的截断版本。他们的工作开启了对截断 theta 级数的新研究，并激发了几位数学家研究该主题。2019 年，Merca 研究了 Rogers-Ramanujan 函数，并在涉及 Rogers-Ramanujan 函数的截断级数上提出了三组猜想。在本文中，我们提出了一种统一的方法来证明 Merca 根据 Pólya 和 Szegö 的结果给出的三组猜想。