A normal form and integration in finite terms for a class of elementary functions
type: Item
instance of: scholarly article
title: A normal form and integration in finite terms for a class of elementary functions
zbMATH Open document ID: 0553.12012
author: Hernan Cendra
published in: Pacific Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: 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 \(\mathbb{C}\{x\}^E\).
Mathematics Subject Classification ID: 12H05
Mathematics Subject Classification ID: 68W99
Mathematics Subject Classification ID: 33B10
Mathematics Subject Classification ID: 12F99
zbMATH DE Number: 3880837
zbMATH Keywords: elementary functions
zbMATH Keywords: exponential field
zbMATH Keywords: exponential ring extension
zbMATH Keywords: integration-in-finite-terms algorithm
MaRDI profile type: Publication
full work available at URL: pjm.1986.121.51
OpenAlex ID: W1997018756
DOI: 10.2140/PJM.1986.121.51
description: scientific article; zbMATH DE number 3880837