The Riemann surface of the r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r$$\end{document}-Lambert function

The r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r$$\end{document}-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.