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Catalogue Information
Field name	Details
Dewey Class	511.1
Title	D-Finite Functions (EBook /) / by Manuel Kauers.
Author	Kauers, Manuel
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2023.
Publication	Cham : : Springer Nature Switzerland : : Imprint: Springer, , 2023.
Physical Details	X, 664 p. 1 illus. : online resource.
Series	Algorithms and computation in mathematics ; 30
ISBN	9783031346521
Summary Note	Defined as solutions of linear differential or difference equations with polynomial coefficients, D-finite functions play an important role in various areas of mathematics. This book is a comprehensive introduction to the theory of these functions with a special emphasis on computer algebra algorithms for computing with them: algorithms for detecting relations from given data, for evaluating D-finite functions, for executing closure properties, for obtaining various kinds of “explicit” expressions, for factoring operators, and for definite and indefinite symbolic summation and integration are explained in detail. The book comes “with batteries included” in the sense that it requires no background in computer algebra as the relevant facts from this area are summarized in the beginning. This makes the book accessible to a wide range of readers, from mathematics students who plan to work themselves on D-finite functions to researchers who want to apply the theory to their own work. Hundreds of exercises invite the reader to apply the techniques in the book and explore further aspects of the theory on their own. Solutions to all exercises are given in the appendix. When algorithms for D-finite functions came up in the early 1990s, computer proofs were met with a certain skepticism. Fortunately, these times are over and computer algebra has become a standard tool for many mathematicians. Yet, this powerful machinery is still not as widely known as it deserves. This book helps to spread the word that certain tasks can be safely delegated to a computer algebra system, and also what the limitations of these techniques are.:
Contents note	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.
Mode of acces to digital resource	Digital reproduction.-
	Cham :
	Springer International Publishing,
	2023. -
	Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-3-031-34652-1
Links to Related Works	Subject References: Computer Science . Differential Equations . Discrete Mathematics . Symbolic and Algebraic Manipulation . Authors: author . Kauers, Manuel . Corporate Authors: SpringerLink (Online service) . Series: Algorithms and computation in mathematics . Classification: 511.1 .

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D-Finite Functions

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