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1、st31EDITIONCRCstandardMathematicALTABLESandformulaeDANIELZWILLINGERCHAPMAN&HALL/CRCACRCPressCompanyBocaRatonLondonNewYorkWashington,D.C.©2003byCRCPressLLCEditor-in-ChiefDanielZwillingerRensselaerPolytechnicInstituteTroy,NewYorkAssociateEditorsStevenG.KrantzKennethH.R
2、osenWashingtonUniversityAT&TBellLaboratoriesSt.Louis,MissouriHolmdel,NewJerseyEditorialAdvisoryBoardGeorgeE.AndrewsBenFusaroPennsylvaniaStateUniversityFloridaStateUniversityUniversityPark,PennsylvaniaTallahassee,FloridaMichaelF.BridglandAlanF.KarrCenterforComputingSc
3、iencesNationalInstituteStatisticalSciencesBowie,MarylandResearchTrianglePark,NorthCarolinaJ.DouglasFairesAlMardenYoungstownStateUniversityUniversityofMinnesotaYoungstown,OhioMinneapolis,MinnesotaGeraldB.FollandWilliamH.PressUniversityofWashingtonLosAlamosNationalLabS
4、eattle,WashingtonLosAlamos,NM87545©2003byCRCPressLLCPrefaceIthaslongbeentheestablishedpolicyofCRCPresstopublish,inhandbookform,themostup-to-date,authoritative,logicallyarranged,andreadilyusablereferencematerialavailable.Priortothepreparationofthis31stEditionoftheCRCS
5、tandardMathematicalTablesandFormulae,thecontentofsuchabookwasreconsidered.Thepreviouseditionwascarefullyanalyzed,andinputwasobtainedfrompracti-tionersinthemanybranchesofmathematics,engineering,andthephysicalsciences.Theconsensuswasthatnumeroussmalladditionswererequir
6、edinseveralsections,andseveralnewareasneededtobeadded.Someofthenewmaterialsincludedinthiseditionare:gametheoryandvotingpower,heuristicsearchtechniques,quadraticelds,reliability,riskanalysisandde-cisionrules,atableofsolutionstoPell’sequation,atableofirreduciblepolynom
7、ialsin ,alongertableofprimenumbers,aninterpretationofpowersof10,acol- lectionof“proofswithoutwords”,andrepresentationsofgroupsofsmallorder.Intotal,therearemorethan30completelynewsections,morethan50newandmod-iedentriesinthesections,morethan90distinguishedexamples,a
8、ndmorethanadozennewtablesandgures.Thisbringsthetotalnumberofsections,sub-sections,andsub-sub-sectionstomorethan1,000.Withinthosesec
