Written by one of the leading specialists in the area, this text is currently the only one to treat this part of symbolic asymptotics. It contains a good deal of interesting material in a new, developing field of mathematics at the intersection of algebra, analysis and computing, presented in a lively and readable way. The associated areas of zero equivalence and Hardy fields are also covered. Due to its clear presentation, this book is interesting for a broad audience of mathematicians and theoretical computer scientists.

Klappentext

Accessible to anyone with a good general background in mathematics, but it nonetheless gets right to the cutting edge of active research.

Some results appear here for the first time, while others have hitherto only been given in preprints.

Inhalt

Zero Equivalence.- Hardy Fields.- Output Data Structures.- Algorithms for Function Towers.- Algebraic Differential Equations.- Inverse Functions.- Implicit Functions.- Star-Product Expansions.- Oscillating Functions.- References.