A normal form and integration in finite terms for a class of elementary functions
Let \(\mathbb{C}\) be the field of complex numbers, \(E\) the usual exponential on \(\mathbb{C}\). So (\(\mathbb{C},E)\) is an exponential field. We define an exponential ring extension \(\mathbb{C}\{x\}^E\) of (\(\mathbb{C},E)\) and give a functional representation: \(\mathbb{C}\{x\}^E\) is isomorphic to the smallest exponential ring extension of (\(\mathbb{C},E)\) containing the functions \(x^s\), \(x\) a real and positive variable, and \(s\in\mathbb{C}\). Finally, we give a simple integration-in-finite-terms algorithm for elements of \(\mathbb{C}\{x\}^E\).
scientific article; zbMATH DE number 3880837