由[tex=9.143x1.357]c4uyRCEJMQT1jWIZcPqabOhGwjrltKDCmykj/bhOD4E=[/tex]求解析函数[tex=4.714x1.357]QWSXe8P/RZYscrdBo9o/lQ==[/tex].

2022-06-19

由[tex=9.143x1.357]c4uyRCEJMQT1jWIZcPqabOhGwjrltKDCmykj/bhOD4E=[/tex]求解析函数[tex=4.714x1.357]QWSXe8P/RZYscrdBo9o/lQ==[/tex].

答案：

因[tex=9.286x2.643]9tO/e5DyKRkzg0MpCtFEonl05vHBsYF+Ad0O5nyxa0L/WiMHgUpMmOoDLpsAWCF9MyRvLITHLrLsVCwrM5DD6kHqfmbNhMOYFthwKvg7lZI=[/tex],由[tex=1.857x1.357]BGkv0wKMIn2R4tUsMDFEFA==[/tex]的解析性,有[tex=9.429x2.643]OTYtdAptVAXC+ZYqi3USUJ3HRWMDOqPTXzlSvbr6pPx9wEZe7A9ie0OXknCbinXYYyIinwFQyoQHw+LYrOYQfMHP72h7s1NZ3UnNQJt02YI=[/tex],[tex=14.929x2.643]7wqf0YjFW8YKKozH12hrl/fgotf0vBxXsva+MxzegSk5QzKgDKnuSPmqnEuIac4W[/tex].又[tex=5.714x2.643]OTYtdAptVAXC+ZYqi3USUJcVUS85OJU+6MaZYH13AAIA65JVW27NtAC0AUSw2iAURh7ncWPoKRASnCL8wfZAFA==[/tex],而[tex=4.429x2.643]OTYtdAptVAXC+ZYqi3USUPVPbRkHaIvv9TBmFFvO/7C17pe9u4zpUAvEBSoMTgA4[/tex],所以[tex=9.5x1.5]LI1BFpbienLi9YM0r+OtCEBeFBmJzZwG1QWtweqSSJwRHwZHhSF9LB0uv22Fd1Xa[/tex].则[tex=8.286x1.5]j/ZK94zh4Fu6zBsqwB/JVHgm1/vGYNsLZ7SFYgf7ypA=[/tex].故[tex=15.286x1.571]WtexR3Khy06x30Xa8Sk3u6NzOT/9eURurkY8IBLuZiLCGSfjLdkGYuG7O0Kwfqs1[/tex].由[tex=3.714x1.357]y2fCVUYjPFCbCthfLv+jIQ==[/tex]得[tex=8.357x1.357]oK25OFNWTGpqGSc/SdnjBQ==[/tex],推出[tex=2.0x1.0]H+dM/PXWEYVHD1gLMzVrXw==[/tex].即[tex=14.143x1.571]WtexR3Khy06x30Xa8Sk3u/MiBQPIHbloKdATGk/DfYn9gX2OoC35Gry2mHKe3Z8Y[/tex][tex=11.929x1.571]DgFipycTN1bchgkmYfu0sUJaQ1znIkmp91LnoBNJAuEGJesv3ZDqHf7KdLiFPBaz[/tex].

举一反三

内容

0
若 [tex=6.143x1.571]2Tgmt23zCEDOCwLdhH9oFvtPcAWRq74zm655k3j5apY=[/tex] 是调和函数，试求解析函数 [tex=4.714x1.357]NL3JEbC2IcrRqXO8pcs+Rw==[/tex] 。
1
由下列条件，求解析函数[tex=4.714x1.357]ntwd9SnbwzOsgm8kiKUlNg==[/tex]：[tex=9.5x1.571]OktS8FkZ/VnaqK4/lnbaobmlXTQT6Euf26ty+B9EOcJtdr9iLxrHvHoKcTNGFTAgV4D89k2FVzwiDh6bHTmgXA==[/tex]，[tex=0.857x1.0]m2DKAQtGuc1DyN3zyNlILg==[/tex]为去原点的复平面.
2
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]
3
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.
4
求函数[tex=3.286x1.429]kdT+eIE7CHPynuN6CaN40g==[/tex]（抛物线）隐函数的导数[tex=1.071x1.429]BUw1BPFU3fsJlAl/vt9M9w==[/tex]当x=2与y=4及当x=2与y=0时,[tex=0.786x1.357]Hq6bf3CacUy07X+VImUMaA==[/tex]等于什么?