设 [tex=5.857x1.429]grsiQIxH1QtysS2kXoDoxJ9oQQ3sGxwmnPyqBk/5AuQ=[/tex] 为调和函数,试求其共轭调和函数 [tex=2.786x1.357]GhcMUKWYfCD3K0BhvBKDbw==[/tex] 及解析函数 [tex=9.286x1.357]VXRiOJeOrIGQLgMSad8UR758hPXkWWekuSonG3su3Hk=[/tex].
举一反三
- 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].
- 已知 调和函数[tex=8.0x1.5]y0Wks3OIKcTlWuphcuSrRBvaoKuK0b+PMCqJCkABczE=[/tex], [tex=0.643x0.786]2LwQJcArGuAsQ0k00CwMFw==[/tex]求其共轭调和函数[tex=2.786x1.357]GhcMUKWYfCD3K0BhvBKDbw==[/tex]及解析函数[tex=8.857x1.357]V8B5MzP6n3pNEUxtCgpYSMZw2KaDlNPXFOwkRCPQUAf5pBIUyV+15DhL6vkfRPsS[/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]
- 证明函数[tex=7.214x1.5]S1ftoyHK1niA72U6OK1yRg5tEHfHxeO1QjO4ZoPI0AE=[/tex]为调和函数，求出共轭调和函数[tex=2.857x1.357]oni5YFYZg9r1D8AXbqLQGA==[/tex]与解析函数[tex=4.643x1.357]T1b4MpRp1jts8m/9pqZ81hEEUhkSW+IaVg1mIAJLtGI=[/tex]
- 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.