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].

2022-06-19

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].

答案：

由[tex=5.0x1.357]3wXwuaO4bujbzw9bj5g6GQ==[/tex], 有: [tex=8.071x1.357]SlxZLwZtBzLBZ7IgZ2I4X++2+DKCs/aESd2jrgr8kP0=[/tex].[br][/br]故 [tex=12.857x1.357]ujMo0J47XrQS1JP/GIb+EKNqazMNewGgF3uhKYHPEFoLwRYH9fCBNV+XK4uoPHzk[/tex] [tex=0.5x0.786]pmD1JbahT9zMRAbBNi045A==[/tex] 的全微分为: [tex=6.429x1.286]LycHjhz0jXNWPqlSpLR8ggQi9CT6FcRZlGY/KAEv+IA=[/tex][tex=18.643x1.5]kohINLky441kKIaOKRELptrM174LdChXKm0phtDwERg/MyfWUlhUABIqyStnZzyT[/tex][tex=7.786x1.571]av4eyekkhIPyT2Hbxo8oibgckPUQO6+TYpICydm6RyjqMT5pJdxUZIy77upoWdTc[/tex].所以[tex=7.214x1.5]Vkze0VAY8uMZzZHXkanHA9OvTrgOLcfN1SrfwKohNxM=[/tex].[tex=17.643x6.286]5+n1W6sD+eGrT4uE0SVYaI3m1SJad0dS+M/HLZnQvDhKOlVqa/FK/6lf7WAg5+Ls6Vw8AYT9220mS0Mhwkh5L2Ovp9v7X4+N+ghSejat9ThZwxKUq+NU5Sg5At9wv44fjx02pm+A7SXzrQACU58qlpETUow5DLZ3LIeEnfJ0fV1zqpFv8O6tA2xI0n0kf6BbUGMtKtfoT0xNvtabjU4yoX8/+fJxA4lZRNFbtbuqwZ4=[/tex]由[tex=3.714x1.357]y2fCVUYjPFCbCthfLv+jIQ==[/tex],所以[tex=8.714x1.5]vq5btDGE+YO6kETTVu8DV0dDfPAWgFsAloNlvSh/QXY=[/tex].

举一反三

内容

0
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]
1
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]
2
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]
3
证明函数[tex=7.357x1.5]6fiPBcL0iUH5inRtC3/AALZPJbKDC9g8o1un1ZPf/s8=[/tex]为调和函数，求出解析函数[tex=4.643x1.357]Vk/CVBWmjrgkz3CajpNVVg==[/tex]
4
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].