Integration in Finite Terms: Fundamental Sources

1. Front Matter

   Pages i-vii

   PDF

2. Integration in Finite Terms

   • Maxwell Rosenlicht

   Pages 1-10

3. Comments on Rosenlicht’s Integration in Finite Terms

   • Michael F. Singer

   Pages 11-30

4. Integration in Finite Terms Liouville’s Theory of Elementary Methods

   • Joseph Fels Ritt

   Pages 31-134

5. Comments on J.F. Ritt’s Book Integration in Finite Terms

   • Askold Khovanskii

   Pages 135-199

6. On the Integration of Elementary Functions which are Built Up Using Algebraic Operations

   • Robert H. Risch

   Pages 200-216

7. Comments on Risch’s On the Integration of Elementary Functions which are Built Up Using Algebraic Operations

   • Clemens G. Raab

   Pages 217-229

8. Integration of Algebraic Functions

   • Barry M. Trager

   Pages 230-286

9. Comments on Integration of Algebraic Functions

   • Barry M. Trager

   Pages 287-295

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.

• symbolic computation
• algebraic curves
• computer algebra systems
• algebraic manipulation
• Liouville Theory

• Institute for Algebra, Johannes Kepler University of Linz, Linz, Austria

  Clemens G. Raab

• Department of Mathematics, North Carolina State University, Raleigh, USA

  Michael F. Singer

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.

Policies and ethics