1、DD nkkDzfzzf1Resi2dDnz1zkznc1ckc nkcDkzzfzzf1ddDnz1zkznc1ckc mcmkkmckkzzzazzfdd kkczfazzfkResi2i2d1,1,1,di21 di21Reskckkckazzzazzfzfkk1 i,2argiln1 ,01d1mzzzzmmzzzzzkkkkckckcmkcmkDD 11Resi2dnkkDzfzzfDkzkc 1ResafDkzckc Dnkcczzfzzfzzfkddd1 fazzzazzfmcmkmciRes2 i2 dd1 kczfzzfkResi2d 11Resi2dnkkDzfzzfD c
2、zzfzfdlimi21Res00 RcRzzffdlimi21Res 2 ,01 ,dd!11Res0111mmfmafmmm 001110dd!11Reszzmmmzfzzzmazf1az)()()(010010zzaazzazzazfmmmmmmmzzazzazzaazfzz)()()()()(00101010 非零有限值mmzzazfzz00lim)(!)!1()()(dd001011zzmamazfzzzmmm)()(dd)!1(1lim )(Res011100zfzzzmazfmmmzz zfzzzfzz000limRes一阶极点一阶极点 zzzf zz ,在在z=z0 解析，且解
3、析，且 00zz0是是 的一阶零点的一阶零点 z 000Reszzzf0)(nnmnmazf azRazazfmnnn ,0 ,21am1 ,1azm0111dd!11fmammm)1(1)(nzzf10z)1)(1(1)1(1)(21zzzzzzfnnnnzzzzzfnnz1 )1)(1(1)1(lim )1(sRe211zzfsin1)(nz 0nnznznznzzznzznzzfnz)1(cos1lim )(sin)(lim sinlim)()(lim 354i2)(zzzzfi21 i2i2i24i2)(3323zzzzzzzzzzf8ii811lim )(i2limi)2(sRe3i
4、2i2zzfzfzz8ii81i)2(1lim i21dd!21lim )(dd!21lim)0(sRe302203220zzzzfzzfzzz 11e1zzfz1 ,0zz 10Res ,10Res ,0fz 11 ,1!1e01zzznznnz 11Res ,11Res ,1fz 2Res ,1Res ,1Res ,fz)10(2d1|2zzzz022zz211z zzzf212Oxy1i111111221z1)1(1 )1)(1(1 1111222zOxy1iz1z2 222121221lim )2(1lim sRe22zzzzfzzzz 1i 121i2)(iRes22d2221|2z
5、fzzzz?dxxfba xxfbad czzFdabl1xxyccba,czzFd21,ccbaba tzz 1c2cc20d)sin,(cosxxxRI2xyOz平面1x0zzzzzzRIzidi2,21|11zzxzzxzzxdi1d),(i21sin),(21cos112xyOz平面1x020).1(0 ,dcos11xxI221|21|112 1ii2 2di221/idzzzzzzzzzI202).1(0 ,dcos211xxIzzzzzzzzzzzzzzzIzzzzd)(1(iid )1(id)(1/id1|1|221|221|21 ,/11i1ilim )(1(i)(lim)(
6、sRe2zzzzfzz22121ii2I2121d)(limRRRRxxfIRRRxxfxxfPd)(limd)(dxxfI)(LRRCRzzfxxfzzfd)(d)(d)(n1)(Resi2 d)(limd)(limkkRRCRRzfzzfxxfR-R+RyCR zkORx0|)(|max|)(|max|d|)(|d)(d)(RCCCzzfRRzzfzzzzfzzzzfzzfRRRnkkzfxxf1)(Resi2d)()()(Resi2d)(上半平面kkzfxxf)()(Resi2d)(下半平面kkzfxxf-R+RyCR zkORx;i21i)i)(i)(lim(i)Resizzzfzi)
7、i)(111)(2zzzzfi0z;i21i2I21dxxI)1,2,3,(,1d ;1d022nxxIxxInn1211i11ii)2()!1()22()1(i)(dd)!1(1lim )(i)(dd)!1(1lim(i)Resnnnnznnnznnnnzznzfzznf222122)!1()!22(2i2)!1()!22(i2nnnnInn212)!1()!22(2nnIni2)!1()!22(i2)!1()22()1(12212nnnnnnnn0,de)(imxxfImxLRRCmzmxmzRzzfxxfzzfde)(de)(de)(iiikRmznkkRRCmzRmxRzfzzfxxf
8、i1iie)(Resi2de)(limde)(lim-R+RyCR zkORx0)(,0,0Imzzzfm0de)(limiRCmzRzzf一致地一致地 zfNRzN,0mmRRRzzfzzfmRmRmRmRCmzCmzRRe1 de2 de2 de de)(de)(2/022/0sin0sinii如果如果 m0,应改为下半平面计算应改为下半平面计算sinicoseiRRRz 202sinOy2/2ysiny1).0,0(,dcos022maxaxmxIamamaaIe2i2ei221xaxxaxImxmxde21deRe2122i22ii2eielim ei)(limeResii22ii22
9、iiaazazazazammzazmzazmzaz).0,0(,dsin0222maxaxmxxIxaxxxaxxxaxxImxmxmxdei21 dei21dei21222i0222i0222ixaxxmxdei210222ixxamamamamIe4e4i2i21amazmzazmzmzazamazzzazzazzazze4 iedd eiddeResi2ii222i2222ii0,d)(mxxfI实轴上上半平面)(Resi )(Resi2d)(jkxfzfxxfRjNjjCNjCRxNjxxxRLzzfzzfxxfxxfxxfzzfd)(d)(d)(d)(d)(d)(11111CRC j
10、-RROjxjxjxnkkNjCLRzfzzfIzzfj1100)(Resi2 d)(limd)(lim)(Resi i )e d(ee )e d(d)(d)(10i000iii1e 01ijkkkkxzCkkjkjCxfaaazxzaxzazzfjjj CRC j-RROjxjxjx实轴上上半平面)(Resi)(Resi2 d)(jkxfzfxxfCRC j-RROjxjxjxjkmxjmzkmxxfzfxxfi实轴上i上半平面ie)(Resie)(Resi2 de)(0dsinxxxIxxIxdei21i2eResii21i0zIzz0)(,2dsindsin00mmxmxmxxxmx0)(,2d|sindsin00mxxxmxxmx
