搞了一天的一道题 冷静一下了

原来玩算符可以玩出欧拉-麦克劳林公式

mazeyu posted @ 2015年5月10日 01:31 in 数学 , 1143 阅读

我太弱是参考这篇的 就不手推了

www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1155-7.pdf

以前我知道的算符其实只有微分算符 可以很神奇的写出幂级数一样的东西

现在发现差分算符也有这样的性质 甚至是移位算符

而且差分算符△与微分算符D的关系是△=exp D - 1 让我十分惊讶

以前我知道的是比如 y-y'=x可以写成(1-D)y=x,然后y=x(1+D+D^2+D^3+...)=x+1

虽然这只能给出特解但也挺神的了

现在知道了欧拉迈克劳林公式的伯努利数原来是通过1/(exp D - 1)扯出来的 真是很神啊

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