LEADER 03964nam 22006255 450 001 9910760255203321 005 20250602122331.0 010 $a3-031-34652-1 024 7 $a10.1007/978-3-031-34652-1 035 $a(MiAaPQ)EBC30876542 035 $a(Au-PeEL)EBL30876542 035 $a(DE-He213)978-3-031-34652-1 035 $a(CKB)28805083400041 035 $a(EXLCZ)9928805083400041 100 $a20231108d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aD-Finite Functions /$fby Manuel Kauers 205 $a1st ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (669 pages) 225 1 $aAlgorithms and Computation in Mathematics,$x2512-3254 ;$v30 311 08$aPrint version: Kauers, Manuel D-Finite Functions Cham : Springer,c2023 9783031346514 320 $aIncludes bibliographical references and index. 327 $aChapter. 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. 330 $aDefined as solutions of linear differential or difference equations with polynomial coefficients, D-finite functions play an important role in various areas of mathematics. This book is a comprehensive introduction to the theory of these functions with a special emphasis on computer algebra algorithms for computing with them: algorithms for detecting relations from given data, for evaluating D-finite functions, for executing closure properties, for obtaining various kinds of ?explicit? expressions, for factoring operators, and for definite and indefinite symbolic summation and integration are explained in detail. The book comes ?with batteries included? in the sense that it requires no background in computer algebra as the relevant facts from this area are summarized in the beginning. This makes the book accessible to a wide range of readers, from mathematics students who plan to work themselves on D-finite functions to researchers who want to apply the theory to their own work. Hundreds of exercises invite the reader to apply the techniques in the book and explore further aspects of the theory on their own. Solutions to all exercises are given in the appendix. When algorithms for D-finite functions came up in the early 1990s, computer proofs were met with a certain skepticism. Fortunately, these times are over and computer algebra has become a standard tool for many mathematicians. Yet, this powerful machinery is still not as widely known as it deserves. This book helps to spread the word that certain tasks can be safely delegated to a computer algebra system, and also what the limitations of these techniques are. 410 0$aAlgorithms and Computation in Mathematics,$x2512-3254 ;$v30 606 $aDiscrete mathematics 606 $aDifferential equations 606 $aComputer science$xMathematics 606 $aDiscrete Mathematics 606 $aDifferential Equations 606 $aSymbolic and Algebraic Manipulation 606 $aEquacions diferencials lineals$2thub 608 $aLlibres electrònics$2thub 615 0$aDiscrete mathematics. 615 0$aDifferential equations. 615 0$aComputer science$xMathematics. 615 14$aDiscrete Mathematics. 615 24$aDifferential Equations. 615 24$aSymbolic and Algebraic Manipulation. 615 7$aEquacions diferencials lineals 676 $a381 676 $a515.354 700 $aKauers$b Manuel$01438649 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910760255203321 996 $aD-Finite Functions$93600298 997 $aUNINA