Symbolic integration I: Transcendental functions
The second edition of Bronstein's excellent book [Algorithms and Computation in Mathematics. 1. (Berlin: Springer). (1997; Zbl 0880.12005)]; the second volume is still missing) contains a new chapter on parallel integration (also called the new Risch algorithm or the Risch-Norman algorithm) This alternative approach to integration attempts to avoid the highly recursive nature of the ``classical'' algorithms described in the first nine chapters. This method was introduced 1976 by \textit{R. Risch} and \textit{A. C. Norman} [Proc. 4th Int. Coll. Adv. Comput. Meth. Theor. Phys, Marseille (1977)] and is used in some computer algebra systems, mostly as a preprocessor for the complete integration algorithm: It is heuristic rather than algorithmic as in some cases it may fail to compute elementary antiderivatives. The first nine chapters of the book contain some improvements and a couple of additional exercises. Bronstein's book still presents the state of the art in the domain of integration of transcendental functions. Its unique blend of detailed mathematics and clear description of algorithms make it both a standard reference and a handbook for researchers and designers of computer algebra systems and a useful, easy to read textbook for teachers and students.
scientific article; zbMATH DE number 2122031