Handbook of Continued Fractions for Special F

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1、HandbookofContinuedFractionsforSpecialFunctionsAnnieCuyt·VigdisBrevikPetersen·BrigitteVerdonk·HaakonWaadeland·WilliamB.JonesHandbookofContinuedFractionsforSpecialFunctionsWithcontributionsbyFrankyBackeljauw·CatherineBonan-HamadaVerifiednumericaloutputStefanBecuwe·AnnieCuyt123An

2、nieCuytUniversityofAntwerpDepartmentofMathematicsandComputerScienceBE-2020AntwerpenBelgiumVigdisBrevikPetersenSør-TrøndelagUniversityCollegeFacultyofTeacherandInterpreterEducationNO-7004TrondheimNorwayBrigitteVerdonkUniversityofAntwerpDepartmentofMathematicsandComputerScienceB

3、E-2020AntwerpenBelgiumHaakonWaadelandNorwegianUniversityofScienceandTechnologyDepartmentofMathematicalSciencesNO-7491TrondheimNorwayWilliamB.JonesUniversityofColoradoDepartmentofMathematicsBoulder,CO80309-0395USAISBN:978-1-4020-6948-2e-ISBN:978-1-4020-6949-9LibraryofCongressCo

4、ntrolNumber:2007941383c2008SpringerScience+BusinessMediaB.V.Nopartofthisworkmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,microfilming,recordingorotherwise,withoutwrittenpermissionfromthePublisher,withtheexceptio

5、nofanymaterialsuppliedspecificallyforthepurposeofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthework.Printedonacid-freepaper987654321springer.comTABLEOFCONTENTSPreface............................................................xiNotation.............

6、............................................xiii0Generalconsiderations......................................10.1Partone.................................................10.2Parttwo.................................................20.3Partthree....................................

7、...........2PartI:BASICTHEORY1Basics.........................................................91.1Symbolsandnotation....................................91.2Definitions..............................................101.3Recurrencerelations....................................131.4E

8、quivalencetransformations............................151.5Con