3楼: Originally posted by hank612 at 2016-01-20 14:36:15
http://math.stackexchange.com/questions/106965/how-to-evaluate-the-integral-of-exp-x2-1-x2-on-0-infty

完全一样的思路， 不妨设z>0, 要证明I:=\int_{0}^{\infty}e^{-(u-\frac{z}{2u})^2}du=\frac{\sqrt ...

2楼: Originally posted by 001gqs at 2016-01-20 14:15:17
首先，左边的积分是收敛的，容易说明。
1. 变量替换：u---->|z/2|/t，得到
    \int exp(-u^2-|z/2|^2/u^2)du=|z/2|*\int exp(-t^2-|z/2|^2/t^2)/t^2 dt
2. 由1得到：
    2*\int exp(-u^2-|z/2|^2/u^2)du= ...