将[tex=8.5x2.643]Kfg3W6cYFVuHUe+hRvsa0BhvbvgpdzOPtJvRFC95JzxUvVlukE7lJlk7o22tzVeP[/tex]在环域[tex=6.0x1.357]nwrhdUAwulozUW5d8OdoXg==[/tex]内展开为洛朗级数.

2022-05-26

将[tex=8.5x2.643]Kfg3W6cYFVuHUe+hRvsa0BhvbvgpdzOPtJvRFC95JzxUvVlukE7lJlk7o22tzVeP[/tex]在环域[tex=6.0x1.357]nwrhdUAwulozUW5d8OdoXg==[/tex]内展开为洛朗级数.

答案：

[tex=31.714x2.857]Kfg3W6cYFVuHUe+hRvsa0PZTCboAsma7xVD+zlMzYtrDKAPiyDBpndaJM7kUDqFQWiRgZ3dhMvCTsk4SPwJId7kOdpVH2HLZ+z2GSj2G4LqbIQKvcGjFutDGInI1OnbOS8t7p+qLw33SMnGlyKtsk4OMdSu1J+l4krTjDekFn2rbJi/BzTLjIvpF3f676tSL6qaKQI5jjQ35uwl07R3UQ7gYj4O8lYrRngjgJU/7ugdpm7nKpVC2huXOdYgthlQp[/tex]由于[tex=6.0x1.357]nwrhdUAwulozUW5d8OdoXg==[/tex]，则[tex=4.571x2.786]yPspLG8wC7r2FyOP8QSW2hLe7PIb3anZjz4VntBQyp453vbWx8Hsr3TyXOpl5JZH[/tex]，故[tex=10.857x2.786]YwPAsex2EZ+URTZaB6+aYrbuO3oJ5VctNYrfyWwZt4ue9mz49Ls/AawyVpxfXVDvUMhcznjMj8xAukRlCtf3JfNa8IkvOlE7XqDLFynynW/P97x868vS2/pt7LuaGJIl[/tex].于是[tex=5.286x2.643]Kfg3W6cYFVuHUe+hRvsa0FyxrEbl1cEIo4eGdLFSKyk=[/tex]在[tex=6.0x1.357]nwrhdUAwulozUW5d8OdoXg==[/tex]内展开式为[tex=17.929x2.786]SXoHoakjgMFXe88HmyTcfdzGrEnf8dlCQ7E8b3BHbBZ3aNJwlSEHzR8E95ZBFYWtF7qVpw2GYBQ8aQxZ4MEHKvNxHmoEKruBrmR2y2AW2HE=[/tex]，[tex=6.786x1.357]cN5qmteoYroqkSkPGXAWrw==[/tex].

举一反三

内容

0
将[tex=7.929x2.643]XPPC+tMm1G1naZHNf9sVbIM6Tck33PGOABGbAzcC/G4=[/tex]展开为洛朗级数，其中[tex=3.429x1.357]sdiWD3CULQhYzL7OdjxVWw==[/tex]，[tex=1.429x1.214]HCTRLtzxkeBZo1HKwKR3/g==[/tex]都是复数.圆环域为：[tex=3.357x1.357]ISWZV5gUmYE5+FjnLXlAtg==[/tex].
1
将函数 [tex=3.429x2.214]iUxHgAMQE7qhTr7AHu7LKv59xiYS9Vot6+Oofvvr4qo=[/tex] 在圆环域 [tex=7.286x1.357]OyuIXkshspt3Q0pAIgQv40cR/wcTi9y71WoZxu8e9wo=[/tex] 内展成洛朗级数.
2
将下列各函数在指定圆环内展开为洛朗级数.[tex=8.357x1.571]HLpLYVDawRs0v3rbcrTzMrNzA5SLIa4248Y7cBEp26LH+tjhDdw48dFkdJZ08s3f[/tex]
3
将函数 [tex=4.071x2.214]ibexzFqU5n9sSvQsestB3Qm7CKURIfhKkvd2IIviX/4=[/tex] 在圆环域 [tex=4.643x1.286]/qrF4IIgVzfPT9SGQmt2+w==[/tex],[tex=7.5x1.286]mBm0cWdIfuPKKoytssqW2+hz2s1YZuOiAIrX3+szI4I=[/tex] 内展成洛朗级数.
4
判断下列命题是否为真：（1）[tex=3.643x1.357]/5abqJjwKZ1qr+6hsVFF5EBvfq3ggOFNlHMClz0h9nk=[/tex]（2）[tex=2.929x1.357]rGJpyjIjJpbcoBTWxP0Jiw==[/tex]（3）[tex=4.5x1.357]2wycHMoqU83MyEp17iBils58bR7YLuCTI2G9NVAdlfY=[/tex]（4）[tex=5.214x1.357]CTz2gu+IIm1GgNmYMGaduCRtA41wnW4WqwRWwEhq6aA=[/tex]（5）[tex=4.857x1.357]1DcE2BMMOaZhTuxR/mjgsboXxfg5ET59Dp4I/jjEDuw=[/tex]（6）[tex=4.643x1.357]BSryrsQYOvTP2hTWRu6t4nAuJwlSs4L9jaq70EpB+Us=[/tex]（7）若[tex=6.0x1.357]y0IZLUnBO88nR8WBZYvd7QXv5S1OMINV5cQNzPyiyAc=[/tex]，则[tex=3.429x1.357]1brfPwTkVVIX4GfoMIUskA==[/tex]（8）若[tex=7.643x1.357]MhLfJXZnhbXiB0x3oNtFzThV4Y1mJxe1VYr7PkJE/T6hmTD3WWp+UxbNwvUQ6DHk[/tex]，则[tex=4.143x1.357]LZUA94ISo1po5HWsOVeBCjo0rMvj7uw3bGw5HiZenrI=[/tex]