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广义积分的无穷级数表示（答疑）

2013-05-17 10:42:17| 分类：数学答疑辅导 | 标签： |举报 |字号大中小订阅

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有两个问题想问您：

1、[e^(-x)]*[cos √ x]对这个函数从0到正无穷积分，为什么等于[（-1）^n ]*n!/(2n)! n从0到正无穷的求和呢？

2、ln (thx) 从0到正无穷的积分等于 -1/[(2n+1)^2] n从0到正无穷的求和？

答：关键是将函数展开成函数项级数，然后逐项积分。详解如下 ：

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