This volume gives an up-to-date review of the subject Integration in Finite Terms. The book collects four significant texts together with an extensive bibliography and commentaries discussing these works and their impact. These texts, either out of print or never published before, are fundamental to the subject of the book. Applications in combinatorics and physics have aroused a renewed interest in this well-developed area devoted to finding solutions of differential equations and, in particular, antiderivatives, expressible in terms of classes of elementary and special functions.
Joseph Liouville: Sur la determination des integrales dont la valeur est algebrique. - Joseph Ritt: Integration in Finite Terms.- Robert Risch: On the Integration of Elementary Functions that are Built Up Using Algebraic Operations.- Barry Trager: Integration of Algebraic Functions.- Maxwell Rosenlicht: Integration in Finite Terms.- Comments to these papers.
Clemens G. Raab is PostDoc at Johannes Kepler University, Linz, Austria. Michael F. Singer is Professor of Mathematics, North Carolina State University, Raleigh, NC, USA.
