复变函数与积分变换参考答案

11TBTTZ2|ZZ222Z51PIZXY2|ZZ2222IXYXYXY0BNVLB2222,XYXYXYZ15B12P/T15I326I1361431I116/5I56/I553222I232I3EE5532COSISIN16316I662666I/43I/21I1I22E8E8I22B31I21/6I2661EE,0,1,2,3,4,5KKKBV616SY,2I23E/6IIE/2I2I23EI/65I2I23E/6I7I23I/E2I23411I/EB40,1,2,22121331/3131KEEK24I64I22IIBV3SY1/31I,127SINI127COS22,12SINI12COS22612/7I662/I6EE45SINI45COS2264/5I6EBMF5S2131PZ083Z11I123382KZEK0,1,2BZ/,3I1,23I1B14/5ZISITMB1|52|Z61|I2|Z3IM2Z40ARGZ7B120IMZ41Z31RE0ZYOXCLA7YUB241ZXY5O1A7YUB16122YZ301REZF50ZF,ZUZH5B20ZF0LIMZZFZAFZBB|0Z15I000|ZZ0,0,ARCTAN0,0,ARCTAN0,ARCTANARGVUUVVUUVUUVZF0,00,01111VUCVUCUC9ZFARGSY1XYP100112222VUXUVXVUUVXUVXVUU0112222VUYUVYVUUVYUVYVUUETIZFLACRHQ00YUVXUUYUUXUV0YUXU9VP0YVXUUVLSY2C3CV7CICCIVUZF32BB5CBVAUAABC,LAB0022BA5NHAABC,BZCBVAUSYXYP00YVBYUAXVBXUAFIVUZFLAUVCRHQ00YUAXUBYUBXUA0YUXU9VP0YVXVFZFBB29S/ZB301ZE43ZN1ZEKKZ21I21ARGI|1|LN1LN“,2,1,0K12SHIZB4SHIZIZE1LNII2,0,1,2,2ZKK“BSINZ0COSZ0LPB1设SINZ0,则EIZEIZ2I0,从而，EIZ21即E2IZ1注意1E02KI故ZK11210PILNI43LNBKK22I2IARGI|I|LNILN“,2,1,0,212IKK2IIARGI|I|LNILNK2I43ARGI|I43|LNI43LNK234ARCTANI5LN211/11212LNLNLNZZZZ21212LN/LNLNZZZZB11212121212LNLN|IARGLNLNIARGIARGZZZZZZZZZZ12LNLNZZ21212121212LN/LN|/|IARG/LNLNIARGIARGZZZZZZZZZZ12LNLNZZB212P2I1E1IEXP4I3II1BEEEEEI2SINI2COS2I2I1111I44441I2EXPCOSISIN1I444EEEEILN3IARG32IILN32ILN33KKEEEE“,2,1,0,3LNSINI3LNCOS2KEKIILN|1I|IARG1I2ILN1I1IKEE22LNSINI22LNCOS2412422LNIKKEE“,2,1,0K12531/L9SIDZZ302B11I3L21L33WL0IMREDZZFDZZFCCTTBAB7ZZF1ZC5ZFX3IC2C1OYZ320REREIICDEEDZZF200ICOSISINCOSD20IIIMIMDEEDZZFC200COSISINSIND13329SDZZZCC_2Z1Y2|Z2|Z4|2ZZZV7ZZ4I422|2|2|4DZZDZDZZZZCZZ334E/SBOOSTB34WL_9/SB1CZDZZE21|2|ZC222CDZZAV|CZAA3I21ZCEDZZV|2I|3/2CZ43CZDZZV|2CZ53COSCZZDZV0CZ“WL62214CDZZZV|3/2CZ7CDZZZ22SIN2|ZC85ZCEDZZV1|ZC1CAUCHYSTCZZZEEDZZEI2I222221CCAZAAZDZAZAZAZDZI1I21222CDZAZDZAZAAZDZ112122I0I221AA3CAUCHYSTIII2I/I2I/1ZZZCCZEDZEDZZEEZZZVV45OT06YFIZCI2ZCCAUCHYST31|I|2231|I|2222414141ZCZZZDZZZDZZZDZ31|I|231|I|2I4I1I4I1ZZDZZZZDZZZZI2I24I1I24I1I2ZZZZZZ033147PT0SINI22SIN22ZCZDZZZ8PT4052II|412ZZZCEDZEZV359/5110SINZZDZ2I0IZZEDZ11100SINSINCOS|SIN1COS1ZZDZZZZ2II00II1|1COS1ISIN11ZZZEDZZE369/S12123COS,|2|3CCCZDZCZCZZV_121200333COSCOSCOS2I2ICOS|COS|022ZZCCCCCZZZDZDZDZZZVVV当N0时，由CAUCHY积分定理，有积分值为零。下面假设N0，由高阶导数公式有H|Z|1EZZNDZH|Z|1EZZ0N11DZ2IN1EZN1|Z02IN137令C是一条以0为心，以RB12222363,363XYUXXYYUXXYY522222I363I36331XYFZUUXXYYXXYYIZ31I,FZIZCC22222222222222222I1IIYXXYXYXYXYZFZVVXYXYXYZZZ111,202FZCFFZZZ53I22I12I1I2I1XYFZUUYXXYZ22I1,2II1FZZCFFZZ54222222I1IIYXXYXYZFZVVXYXYXYZZZLN,FZZCCB311TIFZUVBFK1IFZ9F2UVF3222222222|44|XXFZFZUVFZXYB1IIFZVU7IFZUVBF,UVCRZ7XYVUYXVUBIFZ9FB2IFZUVBFIIFZVUBUVFB312UVFTVUFU9VFBIBI3115B32222222222|FZFZUVXYXY222222222222244|XXYYXXYYXXYYXXUVUVUUUVVVUVFZ1P/TFU1,UFAXBYAB2YUFXB122,XXXYUAFUAFUBF70XXYYUU50F12FCAXBYCB22234211,2,XXXYYYYYUFUFFUFUFXXXXX70XXYYUU52122120,ARCTANYYYFFFCCXXXB16541/NLTLPK11I1INNN2I11NNN3I/21NNEN12221I12I1I11NNNNNNN212LIM1,LIM011NNNN2NLLIM1NN2NL1NN3I/2111COSISIN22NNNNENN11LIMCOS0,LIMSIN022NNNNNLLIM0NN42/LL11INNN2165I8NNN32COSI2NNNB1ICOSISIN22NNN1COS2NNN1SIN2NNNLPL1INNNLI1NNN1INNNHQL172Y65I6188NNN71618NNL165I8NNNL3Y7COSICHNNCHLIM02NNN2COSI2NNNB43P/L11NPNZPN21NNNNZN301NNNIZ41LNINNZNB11/LIMLIM1NPNNNNRA18211111/LIMLIMLIM01NNNNNNNNAANRAA31/LIMLIM1/|1I|1/2NNNNRA61/LIMLIM|LNI|NNNNRA44/FZ7ZILB1311Z32211Z652SIN2ZEZ1ZZE7Z11SIN11|,1113246/FZ7LAURENTB12112ZZ2|1BCFZDZ“B110211221,|11NNNZZZZZZZZZZ1CFZDZ“2IB123231111111,|111NNNZNZZZZZZBCFZDZ“B25120011112,|21211NNNNNZZZZZZZZZCFZDZ“2IB551A/FTITB12211ZZ23SINZZ31123ZZZ4ZZ1LN5211ZZZE611ZE7211ZZE8NNZZ12921SINZ12211FZZZF221ZZ00ZIZB70ZIZB2Y30SINLIMZZZ5BZE0ZAB,7,B0ZSINZ0Z3Z0Z3SINZZBB2300SINSINLIMLIM10ZZZZZ0Z3T11111122ZZZZ1Z71ZBB4A01111LNNNNNZZ1|00ZZF1M,B5ZZZZFM000Z5ZZZZZZMZFMM010ZZZZMZZM010M1,B0ZZF53F0Z2SINSH2ZZZ00SINSH20,SINSH2COSCH20ZZZZZZZZ0SINSH2SINSH0,SINSH2COSCH0ZZZZZZZZZZZZ4500SINSH2SINSH0,SINSH2COSCH2ZZZZZZZZZZFSIN,90ZSH2ZZZ2SINSH2ZZZEB2755P/FKZF1212ZZZ2241ZEZ34211ZZ34COSZZ51COS1Z621SINZZ12011RES,0LIM22ZZFZZZZ2213RES,2LIM222ZZFZZZZ2421ZEZFZS,S0B,0ZZFB423220121LIM0,RESZEZDZDZFZZ34Z7“3248314212111ZZZZZF340,RES1CZF3243223I11RES,ILIMII218ZDZFZZDZZ3243223I11RES,ILIMII218ZDZFZZDZZ412RES,12COS2KZKZFZKKZ0,1,2,K“52011COS,|1|0121NNNZZNZ1RES,10FZC61222111SIN,|021NNNZZZZNZ11RES,06FZC569/S|_13|2SINZZDZZV222|21ZZEDZZV33|21COSMZZDZZVM45|3TANZZDZV6O|B1,|1,|ABANM00,RES1CZF0IH212NM1/12/10,RES231MNZFMNN1I/2123MIMV3HM3212I/1MIMZZZZZZZZF41Z111411444ZZZZZZ4111111411114646164111112426ZZZZZAN,01C0,RESZF9V5IVB589/SC_B2152243,|312CZDZCZZZV1131ZCZEDZZV2|ZC321NNCZDZZVBN|1CZRBF1522412ZZZ3|“3ZYN5IV15224322243112IRES,2IRES,01212IRES,02I112CZDZFZFZZZZZZZV1ZEZZZF1311Z0Z1ZB70Z02211DXX3042401XDXX52COS45XDXXX62SIN1XXDXXBFS53SIN02,Y7SILB22|1|1I3122IRES,1I310I3532I22I610I2ZZZDZIDZZZZZZZVVI3FZFSCOSAB02,Y7SILB222222222|1|11I12I2IRE,0RES,1I222ZZZDZZAABZIDSFZZZZBZAZBBABZVV2222220133IRES,02ZZAAZBZZAFZBAZBZB2222222222I1IRES,432AABZBAABZABFZBZBAB2222IAABBBF2211FZZ2IO223II12RES,ILIMILIMI2I4ZZDDFZZFZDZDZZI2211DXX“2IRES,I2FZB4IFF224401121XXIDXDXF241ZFZZBI3I44,EEOI423I1IRES,4442ZEZFZZ3I4233I1IRES,4442ZEZFZZ1I3I2IRES,RES,24422IFZFZBI245XEIDXXX72145RZZZ52IZBZR31I1I2ISIN2ICOS2RES,I242ZZZEERZEZ5S“BI1RE2IRES,2ICOS2ZRZEE6I21XXEIDXX721ZZZR5IZZRB2IIILIMI,RES1IIIEZZZEZEZRZZZII,RESI21IEEZRIZ5S1IMIE510K/MSLP4S0SINXDXXB0SIN1SIN2XXDXDXXXMUWL9TSBOLBCAUCHYI/ZEZ0ZI/ZEZ105MRRRRYXORICRIIIIIIIIII0RZXZZZXRRRRRRRCRRRREEEEEEDZDXDZDZDZDXZXZZZX7XT5IXXRRRREEDXDXIXXIISIN2IXXRRRRRREEDXDXDXXXXXBIIII22I2IZXRRRRRRRRRRREEEDZDXDXEZXRXRIIILIM0ZRRRRREDZZIIII22001IIZRYYRRRRREEEDZDYDYZRYRYRERII1ZRRRREEDZZRIIIILIM0ZZRRRREEDZDZZZ4“ZEI0LIMIRZCREDZZB320SIN2IIXDXX0SIN2XDXXBFM5S572KFSHQ5TF00COSSINFTATDBTD1COS,1SINAFBFDDJJ11COSJSINCOS22TFTFEDEDFTD00011COSCOSCOSJSINJSIN21COSSINSINSINFDTDFTDATDBTDFDDTYBSINCOSFTDFCOSCOSFTDF71KW82SINFTT1244220,0,1,3SDTETFETFTSTSTYNDTETEDTETFETFSTSSTS02202SIN11110II2I211DTEEEESTTTSIII2111|0I0I2SESEETTSTTSSI1I1I2111II2SESEESSS1111111222SESEESSSB2P/MUFFM12TO2FTTFBO4B3B2BBT34TF1O5AT4A3A2AA1T5BTF4B3B2BB1O1471MTFBF,OBVRTBTTTFSTTF232TT23T322T132232SSS2TFTTE11TTEDSDS12111111SSSSET3TF21TTE221TTTE22DDS2TEDDSTETE23451SSS4TF226SIN6236TETS3666SIN2STM84FTFSNFSREBYNTFTSCTFTFSFT1TIN9/T1FS3SIN2TFTTETPFS30SIN2TTFTTETDTPFS1LN1SFSSPFT30SIN2TTFTTETDPBFSNFSNNDDSFT000NNSTSTNSTDDFTEDTFTEDTTFTEDTDSDS50“REBNTFTSC1TSFTTFTF3SIN2TDTETDS3SIN2TET2222243234SSS32SSDET12SIN0343212SIN23SSTETFSTTF4322SIN203SSDSDDETT222243131232SSSS3211LN2SFSSS2INHTTTS2SINHFTTT4TF301SIN2TTTETDTSTTET2SIN3224334SSS85FTFSSFTFSDSTFTTSFSDSBIN9/TSINKTFTTPFS3SIN2TETFTTPFS21SFSS2PFT30SIN2TTETFTDTTFSPB000STSTSTSSSFTFSDSFTEDTDSFTEDSDTEDTTFTTSFSINSKTTSINKTDU22ARCTAN|SSKUDUUKKARCTAN2SKARCCOTSK2SFSTTTE2SIN3DUTET2SIN3SSUDUU|23ARCTAN432223ARCTAN2S23COTARCS3TTF1221SUDUTUSU112121TTTEETSS41114111411TTSH2514SFSDET12SIN03TTE2SIN3SS1STDUUSDUTE43212SIN2323COTARC123ARCTAN1|SSUSSU869/S102DTTEETT02DTTET2SIN03TDTTET4SINSH02DTTTTETSIN02DTTTETSIN03TDTETT7022SINDTTT23651T00DTTTFDSTF002DTTEETTDSSSDSEETT0221112LN21LN|0SS202DTTET411222SSST3X422SIN2STS22244422SINSSSTT0322316912442SINSTSSTDTTE002SINSH4DTTTTETDSTEEETTTSIN22021DSTETETTSINSIN1212DSSS0221121112121|0012ARCTAN12ARCTAN21SS5212ARCTAN12ARCTAN2181ARCTAN215002SINDTTTET0221SINDSTETDSTET2COS1|0202411LN214111121SSDSSSS5LN416X,11SIN2STS423234242411SINSSSSTT03SINTDTETT042424SIN142313SSSSSTT7002221SINSINDTTTDTTT00022SIN2SINSIN|DTTTDTTTTT00422SINDSSDST22ARCTAN|0SP/B1211TT3TTET45COSSINTTSINSINKTKT67SINHSINHTSINHATAT89UTFATTFATLTDTFFTFTF021211TTD011112TTTTDDTDTT0002333613121TTT3TTTTTDEEDEET00100|TEDEEETTTT4TTDTTDDTTT0002SIN21SIN21COSSINCOSSINTTTTTTSIN212COS41SIN21|05TDTKKKTKT0SINSINSINSINTTKTDDKTK00COS212COS21KTTKTKCOS21SIN21600SINHSINH2TTTTEETTTDDTTTTDEEDEE0022|001212TTTTEEEESINHTT70SINHSINHSINHSINHTATATAATDTTATAAADEEEE022TATTAATTAATTATDEDEEDEEDE0020204111COSHSINH22TATAAT8TDTFAUTFATU0ATH0AUNH0TFATUHTA0ATADTFAUDAFAUTFATU0TADTFYNTADTFATTFATUTA0,09TDTFATFAT0ATH0ANH0TFATHTA0AAATADTFADTFADTFATFAT0AADTFA00AFTDATFTFAYNTAATATFTFAT0,05388P/FFIM1412SSF214SSF3114SSF431SSF59322SSSF6313SSSSF7612SSSSF8134522SSSSF1TF211SFTS2SIN2142212TF31141S3131613TS3341611TSMTFEASFAT1TFSF1TETS34161114TFSF1TES31315TF21SF921SSTTS3SIN3COS29321546TFSF13131SSS231133211SS213S11111STTEE212337TFSF16121SSS3223511SS5352211STTEES3215253318TFSF11345221SSS22132122SS231322221SS221323S222112COS3SIN36COS3SIN333TTTETETETTP/FFIMFI6BZEF1122ASSF2BSASSSF32BSASCSSF4222222ASASSF51322SASSF6BSASSSF17144ASSF822112SSSSSF91122SSSF104122SSSSF1ETFSF12211ASAAA1AATASASIN221EI,RESI,RES2222AASEAASETFSTSTAATAEAEATATSINI2I2IIETF2211ASI1I1I211ASASAI21AI11ASI11ASAATEEAATATSINI21II2ETFSF1BSASS1BBSASSEABSASSESTST,RES,RESBTATBTATBEAEBAABBEBAAE1ETFSF1BSASS1BSBASABA11BA1ABAS11BS11BTATBEAEBA13ETFSF1BBSASECSABSASECSSTST,RES,RES22BSSTATEASCSDSDABEAC2BTBTATEBACATEBABCEBAAC22ETFSF121BSASCS2221111BSBABCBSBACAASBAAC2BAAC211BACAASBAACBS11211BS55BTBTATTEBABCEBACAEBAAC224ETFSF12222212ASAS222212123ASSASAAA2321221ASA221ASSATTATACOS21SIN23ETFSF1I,2RESI,2RES2222222222AEASASAEASASSTSTI222I222I2I2ASSTASSTEASASDSDEASASDSDTATATATATEEATEEAIIII41I4341I43ATTATACOS21SIN235ETF2322111ASAS223111ASSS12A311S1221ASSTTA0322111221DTAS320111SIN22TTAAATD324111COS2TAAATETF32211SASI,RESI,RES0,RES322322322ASASEASASESASESTSTST3I3I02222II2II221AAEAAEASEDSDTATASSTATATACOS11214226ETFBSASS11BSBABASBAASAB1111111AB1BAAS111BABAS111BS11BTATEBABEBAAAB111ETFBSASS11BBSASSEABSASSEBSASSESTSTST,RES,RES0,RES56BTATEBABEBAAAB111ETF4411AS22331211141ASAAASASAATAEEAATATSIN214133ATATASINSH213ETF4411ASI,RESI,RES,RES,RES44444444AASEAASEAASEAASESTSTSTST3I3I33I4I444AEAEAEAETATAATSTATATASINSH2138ETF221112SSSS2112121SSSS11121S2112STTTEE221ETF221112SSSS1,112RES0,112RES2222STSTESSSSESSSS12121SSTESSSDSDTTTEE2219ETFSF111221SSTEESSSTT21111112121TSHTE1,1RES1,1RES0,1RES222222SSESSESSETFSTSTSTTTEESEDSDTTSSTSH2210210ETF41221SSS4131221SSSS31121SSTTSS2COSCOS31421ETF41221SSSI2,41RESI2,41RESI,41RESI,41RES22222222SSSESSSESSSESSSESTSTSTSTI41I4I2I41I4I24II2I4II2I2I22I22I2ITTTTEEEE6666I2I2IITTTTEEEETT2COSCOS31572P/FFIM12241SSF22SSSF32112SSSSSF445124SSSF556912SSSSF6221LNSSSF754222SSSSF822122SSSF922213444SSSSSF10611652232SSSSSSF11463323SSSSSF123231332SSSSSF13221SESFS122141S48142161221SSS161814221S421SSTTT2COS812SIN1612TF21SS2211S11TETS212223TF21121SSSS2,2112RES1,2112RES0,2112RESSSSESSSSESSSSESSTSTST112LIM212LIM2112LIM210SSESSSESSSESSTSSTSSTSTTEE223214TF451241SS12211123164SS411221SS13611121S4221STT2SIN61SIN315TF569121SSS4319121SS9122221323132323131SSSTTETET313132SIN32COS91TETT3132COS32SIN916TFTSS11LN2211221LNSST1TSSS121221SSS21111158TTEETTTCH1221TF221