2018年电大复变函数作业卷(四)

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1、专业好文档复变函数作业卷（四）一、判断题1、数列必收敛。（）解：因为，故级数发散。2、设，则级数收敛的充要条件是级数与都收敛。（√）解：由定理4.1.2知是正确的。3、每个幂级数必在其收敛圆上收敛。（）解：收敛圆上的点发散或收敛需要另行判断。4、若幂级数在点收敛则它必在点收敛。（）解：易知级数在处绝对收敛，而其在处也收敛，故其在以为圆心，以为半径的圆内绝对收敛，在圆上但不能判断收敛还是发散。5、若幂级数在处收敛，则它必在处收。（√）解：易知级数在以为圆心，以2为半径的圆内各点绝对收敛，在圆内，故收敛。二、填空题。专业好文档1、设的收敛域为，则幂级数的收敛域为（）

2、。2、幂级数的收敛圆中心为（），收敛半径为（2）。解：，故收敛半径。3、函数在处所展泰勒级数的半径为（）。解：4、设的罗朗级数展开式为，则其收敛圆环域为（C）。（A）（B）或（C）或（D）三、计算、证明题。1、将函数在处展开成泰勒级数，并指出其收敛半径。解：故收敛半径为。专业好文档2、将分别在下列圆环域内展成罗朗级数（1）解：时，求导得：故（2）解：时，3、将在圆环域内展开成罗朗级数。解：求导得：故专业好文档专业好文档"Ifwedon'tdothatitwillgoonandgoon.Wehavetostopit;weneedthecouragetodoit."

3、HiscommentscamehoursafterFifavice-presidentJeffreyWebb-alsoinLondonfortheFA'scelebrations-saidhewantedtomeetIvoryCoastinternationalTouretodiscusshiscomplaint.CSKAgeneraldirectorRomanBabaevsaysthematterhasbeen"exaggerated"bytheIvorianandtheBritishmedia.Blatter,77,said:"Ithasbeendecide

4、dbytheFifacongressthatitisanonsenseforracismtobedealtwithwithfines.Youcanalwaysfindmoneyfromsomebodytopaythem."Itisanonsensetohavematchesplayedwithoutspectatorsbecauseitisagainstthespiritoffootballandagainstthevisitingteam.Itisallnonsense."Wecandosomethingbettertofightracismanddiscri

5、mination."Thisisoneofthevillainswehavetodayinourgame.Butitisonlywithharshsanctionsthatracismanddiscriminationcanbewashedoutoffootball."The(lackof)airupthereWatchmCaymanIslands-basedWebb,theheadofFifa'santi-racismtaskforce,isinLondonfortheFootballAssociation's150thanniversarycelebrati

6、onsandwillattendCity'sPremierLeaguematchatChelseaonSunday."IamgoingtobeatthematchtomorrowandIhaveaskedtomeetYayaToure,"hetoldBBCSport."Formeit'sabouthowhefeltandIwouldliketospeaktohimfirsttofindoutwhathisexperiencewas."Uefahas openeddisciplinaryproceedingsagainstCSKA forthe"racistbeh

7、aviouroftheirfans"during City's2-1win.MichelPlatini,presidentofEuropeanfootball'sgoverningbody,hasalsoorderedanimmediateinvestigationintothereferee'sactions.CSKAsaidtheywere"surprisedanddisappointed"byToure'scomplaint.InastatementtheRussiansideadded:"WefoundnoracistinsultsfromfansofC

8、SKA."Baumgar