几类常用复初等函数的性质及其应用【摘要】复初等函数是以指数函数为基础的,首先定义了指数函数,之后三角函数,双曲函数,最后定义多值函数中的幂函数,对数函数,和反三角函数.实初等函数与复初等函数有许多类似之处,也有一些不同.通过文章会发现复初等函数定义域扩充到复数域带来的性质变化是很大的.本文主要讲述复初等函数的定义,以及它们各自具有不同与实函数的性质,以及它们在数学解题过程中的应用.【关键词】复初等函数单值函数解析函数1ThePropertiesofSeveralKindsofComplexElementaryFunctionsandtheirApplications【Abstract】ComplexElementaryFunctionsarebasedonexponentialfunctions.Thispaperfirstdefinesexponentialfunction,followedbytrigonometricfunction,hyperbolicfunction,logarithmicfunction,andfinally,powerfunctionandinversetrigonometricfunction.Therearemanysimilaritiesanddifferencesbetweenrealelementaryfunctionsandcomplexelementaryfunctions.Throughthethesis,itcanfoundthattheextensionofthedefinitiondomainofcomplexelementaryfunctiontothecomplexdomainbringsgreatchangesinnature.Itmainlyintroducesthedefinitionofcomplexelementaryfunctions,theirdifferencesandthepropertiesofrealfunctions,andtheirapplicationsinsolvingmathematicalproblems.【Keywords】ComplexElementaryFunctions;UniformFunction;AnalyticFunction23目录1引言...........................................................................................................................................12初等解析函数...........................................................................................................................12.1常数函数.......................................................................................................................................12.1.1常数函数的定义....................................................................................................................12.1.2常数函数的性质....................................................................................................................12.1.3常函数的应用........................................................................................................................12.2指数函数.......................................................................................................................................22.2.1指数函数的定义....................................................................................................................22.2.2指数函数的性质....................................................................................................................22.2.3指数函数的应用....................................................................................................................22.3三角函数......................................................................................................................................32.3.1三角函数定义........................................................................................................................32.3.2三角函数的性质....................................................................................................................32.3.3三角函数的应用....................................................................................................................42.4双曲函数.......................................................................................................................................42.4.1双曲函数的定义............................
