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关于展开为傅里叶级数和傅里叶贝塞尔级数的问题

2018春140201LFJ
在这次作业中遇到了一些级数展开问题
image
还有一个是右边等式为
image
对于第一个可以先傅里叶展开再用傅里叶贝塞尔级数求得A
但是对于第二个
image
展开时涉及到周期延拓问题,怎样才能进行合理的延拓(已参考书,说是延拓到4L的周期)

关于默比乌斯变换

课上关于默比乌斯变换的讨论,当时没说清楚
是不是这样的,设一个莫比乌斯变换的矩阵为(a b; c d)(是2阶方阵)
c=0时:这个变换仅仅是有限的平移、旋转、位似变换的叠加,直线映射为直线,真正的圆映射为真正的圆
c≠0时:
如果一个广义圆过-d/c这个点,他一定被映射为直线(不论他本身是任何种类的广义圆)
如果不过-d/c这个点,他一定被映射为真正的圆(同样的,不论他本身是任何种类的广义圆)

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