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]
举一反三
- 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]
- 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]
- [tex=5.143x1.357]2Js34AY0MRDQ2/Apd8rGGA==[/tex]是一个调和函数,求:[tex=2.857x1.357]oni5YFYZg9r1D8AXbqLQGA==[/tex]与[tex=2.786x1.357]dal2CT/ildxtMhXRn1xYUQ==[/tex]组成的解析函数
- 由下列条件求解析函数[tex=4.643x1.357]T1b4MpRp1jts8m/9pqZ81hEEUhkSW+IaVg1mIAJLtGI=[/tex][tex=9.071x1.357]6haMKJs64xtHBC/FnedUjWgEUhUEmTLzKRF7ViVBKDs=[/tex]
- 求下列函数的导函数：(1) [tex=5.0x2.357]X/CieCDGJ7iPQ3YFWuscHxHrcIE/dPFa9tFyiJXze8A=[/tex](2)[tex=6.643x1.714]Oj74y/L+OxY81QME5JWMcl+7PZ2FGQswwvjgVhjq1Dmb6dBU0oAjZBW7eFBVjqo6[/tex]