收敛无穷限广义积分被积函数在无穷远处性质  

Asymptotic properties of convergent infinite integral′s integrand

作　　者：张立柱[1] 

机构地区：[1]上海财经大学应用数学系,上海200433

出　　处：《纯粹数学与应用数学》2012年第3期303-307,共5页Pure and Applied Mathematics

摘　　要：讨论了第一型广义积分收敛时被积函数在无穷远处渐近性质,证明当广义积分收敛时,被积函数在无穷远处不一定趋于零,而可以表现为其他多种形式,如剧烈振荡的连续函数,或间断函数,甚至可以是特殊形式的非负连续函数等.最后给出当广义积分收敛时,判别被积函数在无穷远处是否趋于零时的几个条件.Abstract： In this paper, asymptotic properties of convergent infinite integralls integrand are discussed. It is proved that the limitation of integrand at infinite distance does not equal zero when the infinite integral is convergent, but the integrand can be many other types, such as violent vibrating continuous function, discon- tinuous hmction, or even non-negative continuous function of specialized type. Several conditions are given to distinguish whether the limitation of integrand at infinite distance equals zero or not when the infinite integral is convergent.

关 键 词：广义积分 渐近性质 收敛 

分 类 号：O172.2[理学—数学]