NAG Library Chapter Introductions – Approximations of Special FunctionsIdentification and CharacterizationNAG图书馆课时介绍 特殊函数的S-逼近.pdf

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1、s–ApproximationsofSpecialFunctionsIntroduction–sNAGLibraryChapterIntroductions–ApproximationsofSpecialFunctionsContents1ScopeoftheChapter........................................22BackgroundtotheProblems..................................22.1FunctionsofaSingleRealArgument............................22

2、.2ApproximationstoEllipticIntegrals.............................42.3BesselandAiryFunctionsofaComplexArgument..................52.4OptionPricingFunctions....................................53RecommendationsonChoiceandUseofAvailableFunctions........63.1EllipticIntegrals................................

3、..........63.2BesselandAiryFunctions...................................64Index....................................................65FunctionsWithdrawnorScheduledforWithdrawal...............106References................................................10[NP3678/9]s.1Introduction–sNAGLibraryManual1Scop

4、eoftheChapterThischapterisconcernedwiththeprovisionofsomecommonlyoccurringphysicalandmathematicalfunctions.2BackgroundtotheProblemsThemajorityofthefunctionsinthischapterapproximatereal-valuedfunctionsofasinglerealargument,andthetechniquesinvolvedaredescribedinSection2.1.Inadditionthechaptercontainsf

5、unctionsforellipticintegrals(seeSection2.2),BesselandAiryfunctionsofacomplexargument(seeSection2.3),complementaryerrorfunctionofacomplexargumentandvariousoptionpricingfunctionsforuseinfinancialapplications.2.1FunctionsofaSingleRealArgumentMostofthefunctionsprovidedforfunctionsofasinglerealargumenthav

6、ebeenbasedontruncatedChebyshevexpansions.Thismethodofapproximationwasadoptedasacompromisebetweentheconflictingrequirementsofefficiencyandeaseofimplementationonmanydifferentmachineranges.FordetailsofthereasonsbehindthischoiceandtheproductionandtestingproceduresfollowedinconstructingthischapterseeSchonf

7、elder(1976).Basically,ifthefunctiontobeapproximatedisfxðÞ,thenforx2½a;banapproximationoftheformX0fxðÞ¼gxðÞCrTrðÞtr¼0P0isused(denotes,accordingtotheusualconvention,asummationinwhichthefirsttermishalved)