The \(r\)-Lambert function is a generalization of the classical Lambert W function which has proven to be useful in physics and other disciplines. In this paper we construct the Riemann surface of this function. It turns out that this surface has some peculiar properties, therefore it might be useful for demonstration purposes, for those who would like to see non-standard examples of Riemann surfaces coming from complex function theory.

中文翻译：

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$$r$$ r -Lambert 函数的黎曼曲面

的\（R \） -Lambert功能是已被证明是在物理和其他学科中有用的经典朗伯W函数的推广。在本文中，我们构造了该函数的黎曼曲面。事实证明，这个曲面具有一些特殊的性质，因此对于那些希望看到来自复函数理论的黎曼曲面的非标准示例的人来说，它可能对演示目的很有用。