泊松积分的几种简便证明

Several Simple Methods in Proving Poisson Integral

在一般的《高等数学》教材中对于泊松积分的计算少有涉及,而在实际问题中,例如在研究热传导或是概率问题的时候,都会遇到泊松积分。但由于其被积函数的原函数不是初等函数,因此,不能用牛顿-莱布尼茨公式来计算其积分值。而一般证明方法比较繁锁,笔者在此给出泊松积分的几种较为简便的证明方法。

In generally textbooks of Advanced Mathematics,the methods of solving Poisson integral was less mentioned.It encountered Poisson integral in practical problem usually,such as heat conduction problem or probability problem.It couldn＇t solve integral value with New-leibniz formula,because the primitive function of integrand wasn＇t elementary function.This paper introduces several simple methods of solving Poisson integral,due to its complex in common.