Manuel Kauers studied computer science in Karlsruhe, Germany, from 1998 to 2002 and then went to Linz, Austria, where he received his Ph.D. in symbolic computation in 2005. He won a START prize in 2009. Since 2015 he is director of the Institute for Algebra at Johannes Kepler University in Linz. Kauers is an active member of the computer algebra community and has been contributing to the design, implementation, and application of algorithms for D-finite functions for many years. Together with Christoph Koutschan and Doron Zeilberger, he proved two outstanding conjectures in enumerative combinatorics using such algorithms. For one of these results, the proof of the qTSPP-conjecture, they received the AMS David P. Robbins prize in 2016.

“The aim of this book is to provide a solid foundation for researchers who wish to enter the field of D-finite functions. It offers a comprehensive and self-contained introduction to the theory, computation, and applications of D-finite functions, making it particularly valuable for researchers and graduate students. The book contains many illustrative examples to facilitate the reading of the book.” (Amir Hashemi, zbMATH 07756344, 2024) “The book is written in a precise style with attention to detail. The provided algorithms are in symbolic code, but can be easily (relatively) translated to programs. The exercises are well designed and informative. The book is an excellent source of information and will work best for graduate-level math education, though it may also motivate researchers to apply the theory in their own fields.” (Alexander Tzanov, Computing Reviews, March 27, 2024)

• Chapter. 1. Background and fundamental concepts.- Chapter. 2. The recurrence case in one variable.- Chapter. 3. The differential case in one variable.- Chapter. 4. Operators.- Chapter. 5. Summation and integration.- Answers to Exercises.- Software.- Notations.- References.- Index.

Manuel Kauers studied computer science in Karlsruhe, Germany, from 1998 to 2002 and then went to Linz, Austria, where he received his Ph.D. in symbolic computation in 2005. He won a START prize in 2009. Since 2015 he is director of the Institute for Algebra at Johannes Kepler University in Linz. Kauers is an active member of the computer algebra community and has been contributing to the design, implementation, and application of algorithms for D-finite functions for many years. Together with Christoph Koutschan and Doron Zeilberger, he proved two outstanding conjectures in enumerative combinatorics using such algorithms. For one of these results, the proof of the qTSPP-conjecture, they received the AMS David P. Robbins prize in 2016.

“The aim of this book is to provide a solid foundation for researchers who wish to enter the field of D-finite functions. It offers a comprehensive and self-contained introduction to the theory, computation, and applications of D-finite functions, making it particularly valuable for researchers and graduate students. The book contains many illustrative examples to facilitate the reading of the book.” (Amir Hashemi, zbMATH 07756344, 2024) “The book is written in a precise style with attention to detail. The provided algorithms are in symbolic code, but can be easily (relatively) translated to programs. The exercises are well designed and informative. The book is an excellent source of information and will work best for graduate-level math education, though it may also motivate researchers to apply the theory in their own fields.” (Alexander Tzanov, Computing Reviews, March 27, 2024)

• Chapter. 1. Background and fundamental concepts.- Chapter. 2. The recurrence case in one variable.- Chapter. 3. The differential case in one variable.- Chapter. 4. Operators.- Chapter. 5. Summation and integration.- Answers to Exercises.- Software.- Notations.- References.- Index.