如果[tex=4.714x1.357]k7ZZy29fAPTldYCnWZx7/A==[/tex]为解析函数,试证 [tex=1.357x1.071]og+VaJoemW8SvHvpKGJoig==[/tex]是[tex=0.5x0.786]pmD1JbahT9zMRAbBNi045A==[/tex]的共轭调和函数.
举一反三
- 由已知调和函数[tex=9.143x1.357]R0xF92SKx3DtVs29//bLzCsvUfwh7lR1ivO0LtzTB8M=[/tex]求解析函数[tex=4.714x1.357]k7ZZy29fAPTldYCnWZx7/A==[/tex].
- 由下列已知调和函数，解析函数[tex=4.714x1.357]k7ZZy29fAPTldYCnWZx7/A==[/tex].[tex=5.857x1.429]grsiQIxH1QtysS2kXoDoxJ9oQQ3sGxwmnPyqBk/5AuQ=[/tex].
- 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]
- 在下列各对函数中，[tex=0.5x0.786]pmD1JbahT9zMRAbBNi045A==[/tex]是否为[tex=0.643x0.786]dFKQavWFzybe6S1GPVXNhQ==[/tex]的共轭调和函数：[tex=4.929x1.143]56YM4cGErGSKql+NmkMGAA==[/tex].
- 设[tex=0.5x0.786]pmD1JbahT9zMRAbBNi045A==[/tex]是[tex=0.643x0.786]dFKQavWFzybe6S1GPVXNhQ==[/tex]的共轭调和函数，问：在下列各对函数中，后者是否为前者的共轭调和函数：[tex=4.214x1.429]HUj6fL56FyetAOgbEDmfSereI3mBHRGeQtJkHCLtAaw=[/tex].