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010   $a1-4471-6464-4
024 7 $a10.1007/978-1-4471-6464-7
035   $a(CKB)3710000000143766
035   $a(EBL)1781968
035   $a(SSID)ssj0001276063
035   $a(PQKBManifestationID)11951246
035   $a(PQKBTitleCode)TC0001276063
035   $a(PQKBWorkID)11239195
035   $a(PQKB)10346409
035   $a(DE-He213)978-1-4471-6464-7
035   $a(MiAaPQ)EBC6312976
035   $a(MiAaPQ)EBC1781968
035   $a(Au-PeEL)EBL1781968
035   $a(CaPaEBR)ebr10983297
035   $a(OCoLC)881476472
035   $a(PPN)179767097
035   $a(EXLCZ)993710000000143766
100   $a20140610d2014      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aHypergeometric Summation $eAn Algorithmic Approach to Summation and Special Function Identities /$fby Wolfram Koepf
205   $a2nd ed. 2014.
210  1$aLondon :$cSpringer London :$cImprint: Springer,$d2014.
215   $a1 online resource (290 p.)
225 1 $aUniversitext,$x0172-5939
300   $aDescription based upon print version of record.
311   $a1-4471-6463-6 
327   $aIntroduction -- The Gamma Function -- Hypergeometric Identities -- Hypergeometric Database -- Holonomic Recurrence Equations -- Gosper?s Algorithm -- The Wilf-Zeilberger Method -- Zeilberger?s Algorithm -- Extensions of the Algorithms -- Petkov?sek?s and Van Hoeij?s Algorithm -- Differential Equations for Sums -- Hyperexponential Antiderivatives -- Holonomic Equations for Integrals -- Rodrigues Formulas and Generating Functions.
330   $aModern algorithmic techniques for summation, most of which were introduced in the 1990s, are developed here and carefully implemented in the computer algebra system Maple?. The algorithms of Fasenmyer, Gosper, Zeilberger, Petkov?ek and van Hoeij for hypergeometric summation and recurrence equations, efficient multivariate summation as well as q-analogues of the above algorithms are covered. Similar algorithms concerning differential equations are considered. An equivalent theory of hyperexponential integration due to Almkvist and Zeilberger completes the book. The combination of these results gives orthogonal polynomials and (hypergeometric and q-hypergeometric) special functions a solid algorithmic foundation. Hence, many examples from this very active field are given. The materials covered are suitable for an introductory course on algorithmic summation and will appeal to students and researchers alike.
410  0$aUniversitext,$x0172-5939
606   $aAlgorithms
606   $aComputer software
606   $aSpecial functions
606   $aDifferential equations
606   $aCombinatorics
606   $aAlgorithms$3https://scigraph.springernature.com/ontologies/product-market-codes/M14018
606   $aMathematical Software$3https://scigraph.springernature.com/ontologies/product-market-codes/M14042
606   $aSpecial Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M1221X
606   $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147
606   $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010
615  0$aAlgorithms.
615  0$aComputer software.
615  0$aSpecial functions.
615  0$aDifferential equations.
615  0$aCombinatorics.
615 14$aAlgorithms.
615 24$aMathematical Software.
615 24$aSpecial Functions.
615 24$aOrdinary Differential Equations.
615 24$aCombinatorics.
676   $a515.55
700   $aKoepf$b Wolfram$4aut$4http://id.loc.gov/vocabulary/relators/aut$0481654
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910299989803321
996   $aHypergeometric summation$9253292
997   $aUNINA