Ebook: Symbolic Asymptotics

Symbolic asymptotics has recently undergone considerable theoretical development, especially in areas where power series are no longer an appropriate tool. Implementation is beginning to follow.

The present book, written by one of the leading specialists in the area, 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.

The book is intended to be 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.

Due to its clear presentation, this book is interesting for a broad audience of mathematicians and theoretical computer scientists.

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Symbolic asymptotics has recently undergone considerable theoretical development, especially in areas where power series are no longer an appropriate tool. Implementation is beginning to follow.

The present book, written by one of the leading specialists in the area, 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.

The book is intended to be 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.

Due to its clear presentation, this book is interesting for a broad audience of mathematicians and theoretical computer scientists.

---

Symbolic asymptotics has recently undergone considerable theoretical development, especially in areas where power series are no longer an appropriate tool. Implementation is beginning to follow.

The present book, written by one of the leading specialists in the area, 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.

The book is intended to be 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.

Due to its clear presentation, this book is interesting for a broad audience of mathematicians and theoretical computer scientists.

Content:
Front Matter....Pages I-XI
Introduction....Pages 1-6
Zero Equivalence....Pages 7-41
Hardy Fields....Pages 43-58
Output Data Structures....Pages 59-81
Algorithms for Function Towers....Pages 83-128
Algebraic Differential Equations....Pages 129-153
Inverse Functions....Pages 155-173
Implicit Functions....Pages 175-189
Star-Product Expansions....Pages 191-214
Oscillating Functions....Pages 215-234
Back Matter....Pages 235-243

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Symbolic asymptotics has recently undergone considerable theoretical development, especially in areas where power series are no longer an appropriate tool. Implementation is beginning to follow.

The present book, written by one of the leading specialists in the area, 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.

The book is intended to be 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.

Due to its clear presentation, this book is interesting for a broad audience of mathematicians and theoretical computer scientists.

Content:
Front Matter....Pages I-XI
Introduction....Pages 1-6
Zero Equivalence....Pages 7-41
Hardy Fields....Pages 43-58
Output Data Structures....Pages 59-81
Algorithms for Function Towers....Pages 83-128
Algebraic Differential Equations....Pages 129-153
Inverse Functions....Pages 155-173
Implicit Functions....Pages 175-189
Star-Product Expansions....Pages 191-214
Oscillating Functions....Pages 215-234
Back Matter....Pages 235-243
....