几种反常积分的应用  

Several Applications of Improper Integral

作　　者：朱烈浪[1] 胡建根[1] 

机构地区：[1]江西农业大学理学院,南昌330045

出　　处：《江西科学》2014年第4期501-502,530,共3页Jiangxi Science

摘　　要：给出3种形式无穷限反常积分在概率统计中的应用。以反常积分Γ(α)=∫∞0xα-1e-xdx,(α>0)及Φ(x)=∫x-∞1/2π(1/2)e-t22 dt为例,介绍它们在概率论与数理统计及高等数学学习中的应用,利用反常积分来判断无穷级数的敛散性,计算某些定积分及验证正态分布的结论。可以看出反常积分不只是一个数学概念,其实也是一种数学方法。In this article, we give three types of applications of infinite limit improper integral in probability and statistics. For Г （a） and φ （x） example, we introduce applications of improper integral in probability and mathematical statistics, we use improper integral to judge the divergence of infinite series;to calculate some definite It can be seen that improper integral is of mathematical method. integral and to verify some conclusions in normal distribution. not only a mathematical concept, but it actually is also a kind

关 键 词：反常积分 无穷级数 中心极限定理 

分 类 号：O211.4[理学—概率论与数理统计]