试证[tex=8.786x2.357]TnUDpRqmp498lq23BsppU5DHMFH1fKl7zMotzn8+SyM2n30HbyVGiZLMXCNDIzQC[/tex]都是调和函数,但 [tex=2.214x1.143]hSY9o2OT3oZRiVc2tzqZ/w==[/tex]不是解析函数.
举一反三
- 证明：函数[tex=4.0x1.429]h8L9h8J7AgNi0Vi1+nVgbQ==[/tex]，[tex=4.357x2.357]vpgLV47EHIN8emToP5bea3RiO0Fo1FVZaComJ3NTHss=[/tex]都是调和函数，但[tex=4.714x1.357]QWSXe8P/RZYscrdBo9o/lQ==[/tex]不是解析函数.
- 试证 [tex=8.429x2.357]TnUDpRqmp498lq23BsppU5DHMFH1fKl7zMotzn8+SyOkJWBNIx2+JXJQjyc7JJ7dtHUGnOoPZIOihoG/O95H/Q==[/tex]都是调和函数,但 [tex=2.143x1.143]eAe93E7I9Yk1RqYukuAq3OAgLuEBEyyfW0/J9V3I9ng=[/tex]不是解析函数.
- 如果[tex=4.714x1.357]WVXxmENOyLsrAK1u24ZaKpfiudWoCMFKE7yFzwDqM2w=[/tex]是一解析函数，试证：（1）[tex=2.143x1.786]4KZ/pO3sLF10383T2p50AW8R8WCm4Eix38GcIab+i3pwQwzF+fKFx+fNj5ugVqci[/tex]也是解析函数（2）-u是v的共轭调和函数。（3）[tex=8.929x2.714]VGXzV15psxV0cBMwKVrVbuMoOXdV+Yk2MpPVTJAvfxMCkIE3bPD/y0Sxfc1i847aFfKM2ml7yjnGpx5L1BLATZBsa7LoRJpwet6xLTvJptc4CCpsVuNX5Ot7Bqn2RJCiclGj4NQRw7fbKhp2F0ajXw==[/tex]=[tex=8.857x1.643]Q0Ezd43LDeNGSFF1HD/X+nVEh77NG1HPyrxZMPH3igXsS6p9dc+DNDH3M8YtOEmzDfM1ltfMQmlTNS1Y3AOXC9SS+kODOYzv283/UaXaVtQ=[/tex]
- 试证下列各函数为调和函数,并求出相应的解析函数[tex=4.143x1.357]LogYAzAvCq1eGBWwADRiTDEXgIiuKOaEt6GvKoBkivE=[/tex].[tex=5.714x1.214]VEsoUf4je2PNRlzpzthCydShncrGfk7D2ORDhzaPEW0=[/tex]
- 试证下列各函数为调和函数,并求出相应的解析函数[tex=4.143x1.357]LogYAzAvCq1eGBWwADRiTDEXgIiuKOaEt6GvKoBkivE=[/tex]. [tex=1.929x0.786]wSgNtKeeL9Lp26PWjTxglQ==[/tex]