复变函数阶段练习.pdf

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1、复变函数阶段练习一（第一、二章内容）一、填空题：1.复数iz231的实部 _133_，虚部_132_，模 _1313_，辐角_32arctan_.2.iiiz131的实部是 _23_，虚部是 _25_，模为 _234_，主辐角为 _35arctan_.3i31的指数形式为_32ie_，三角表示式 _3sin3cos2i_.4)32(iLn_kki),223arctan(3ln21为整数 _.5i)1(_)12(ke_.6.,1ze则z_ik2_.二、计算下列各题：1、求下列复数的模和主辐角（1）1+i1+=2i；arg1+=4i（）（2）2+5 i52+5=29 arg2+5=arctan2i

2、i，（）（3）-1+3 i-1+3=10 arg-+3=-arctan 3ii，（1）求6)1(i解：因iei421故iieeiii8)23si n23(c o s322)2()1(235646求083z的所有根.解：83z38z)2,1,0(232kekiizk3100时，,21,1zk时，izk3122时，、求下列各函数值（1）34Lni；（2）lnie；（3）3i解：（1）434ln34arctan23Lniiik4ln 5arctan20,1,3ikk等（2）lnln122ieieii（）ln 3232ln 330,1,iikiiLnkieeek等 已 知 调 和 函 数xyyxyxu

3、22),(，求 其 共 轭 调 和 函 数),(yxv及 解 析 函 数),(),()(yxivyxuzf.xyxyyuxv2)2(所以)(22)2(2ygxxydxxyv)(2ygxyv又yxxuyv2比较两式可得：yxygx2)(2故yyg)(，有Cyydyyg2)(2文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G

4、5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文

5、档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW

6、9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10

7、A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 H

8、S6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7

9、T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10

10、ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9因此Cyxxyv22222（C 为任意常数）因而得到解析函数：),(),()(yxivyxuzfiCyxxyixyyx)222()(2222设22),(yxyxu为调和函数，求解析函数ivuzf)(解：利用C-R 方程，得：xxuyv2所以)(22xgxyxdyv)(2xgyxv又yyuxv2比较两式可得：0)(xg故Cxg)(因此Cxyv2（C 为任意常数）因而得到解析函数：),(),()(yxivyxuzfiCziCiyxCxyiyx2222)()2()(已知)()(cybxiayxz

11、f在复平面上解析，求a,b,c 的值.解：cxvbxvayuxucybxvayxu,1,由 C-R 条件，xvyuyvxu,，得abc,1所以，当abc,1时，)(zf在复平面上解析。文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2

12、K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码

13、:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9

14、T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K

15、3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N

16、7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q

17、10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8

18、T6G5G2K98设yxyxu)1(2),(为调和函数，求解析函数ivuzf)(.解：yux2，)1(2 xuy由 C-R 条件，有：yvy2，)1(2 xvx)(22xgyydyv22)(xxgvxCxxyv222于是，得)2()1(2)(2Cxxiyxzf9已知调和函数yeyxuxsin),(，求解析函数),(),()(yxivyxuzf解：利用 C-R 方程，得：yeyuxvxcos)(coscosygyeydxevxx对 y 求偏导并利用C-R 方程，有)(s i nygyeyvxyexuxs i n于是，知：0)(yg，有Cyg)(因此Cyevxcos（C 为任意常数）因而得到解析函

19、数：),(),()(yxivyxuzfiCyieyexxcossin文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A

20、6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS

21、6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T

22、2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 Z

23、Y8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5

24、G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档

25、编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9复变函数阶段练习二（第三、四章内容）三、填空题：1.212zdzz_0_.2.dzzz1|cos2_

26、0_.3.解析函数)(zf的导函数仍为_ 解析函数_，且)(0)(zfn_rzzndzzzzfin|100)()(2!_.、5.12)1(zzdzze_0_ 5.212iizdz_3311i_ 6.1)1(nnnnz的收敛半径为_1_.7.级数13)1(nnnzn的收敛半径为_3_.8.311z在0z处的 Taylor 展开式为 _03nnz_.9zzf511)(在0z处的 Taylor 展开式为 _0)5()(nnzzf_.四、计算题：1.CzdzRe，其中 C 为由 0 到i1的直线段。解：C 的参数方程为：10)1(titz)1(21)1(Re10idtitzdzCi.计算积分dzzC2

27、其中，C 为连接原点0 到i3的直线段五、解：积分路径的参数方程为titz)3()(（10t），于是，dtidz)3(，因此文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q

28、10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8

29、T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2

30、K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码

31、:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9

32、T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K

33、3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9310322)3(31)3(idtitdzz

34、C3计算积分Cdzzzz1122的值，其中C：2|z.2 解：因12)(2zzzf在2|z上解析，1z在2|z的区域内，由柯西积分公式得：izzidzzzzzz4)12(2112122|24计算积分izdzze0)23(解：43313)3()23(020iiizizeezedzze5计算积分1|22zzdzze解：令zezf2)(，则)(zf在1|z内解析。由高阶导数公式，得：ifidzzezz4)0()!12(221|26求下列幂级数的收敛半径（）12nnnnzi；（）11nnniz。（）11121limlim22nnnnnnanan，收敛半径为2；（）lim12nnni，收敛半径为22。7

35、求下列函数11zz在01z点处的泰勒展开式1221111111211+2zzzzz文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW

36、9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10

37、A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 H

38、S6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7

39、T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10

40、ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G

41、5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K901112nnnz11112nnnz其中112z，即12z8将函数)2)(1(1)(z

42、zzf分别在圆环10z,2|1z,|2z内展开成罗朗级数.8 解：(1)21121111121)(zzzzzf由于1|z，从而12z，利用.1112nzzzz（1|z）得到：00221)(nnnnzzzf222221211zzzz2874321zz（1|z）(2)由于2|1z，11,12zz所以zzzzzzf1111211211121)(0101001211221nnnnnnnnnzzzzz文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 H

43、S6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7

44、T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10

45、ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G

46、5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文

47、档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW

48、9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10

49、A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9(3)由于|2z，11,12zz所以zzzzzzzf111121111121)(010100121121nnnnnnnnnzzzzzz9 设32)1(2)(2zzzzf，求)(zf在3|1z内的 Laurent 展开式。3111)3)(1()1(2)(zzzzzzf当3|1z时，有3113111113111)(zzzzzzf313z)1(31110n0zzznnnn文档编

50、码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K9T10A6K3 HS6N7X7T2Q10 ZY8T6G5G2K9文档编码:CW9K