广义积分敛散性的一点注解  

Comment on the Astringency of Improper Integral

作　　者：张利[1] 

机构地区：[1]安康学院数学系,陕西安康725000

出　　处：《安康学院学报》2009年第3期83-84,共2页Journal of Ankang University

基　　金：陕西省精品课程<高等数学>(2005-80);陕西省教育厅教学改革项目(04G32);安康学院教改项目(Jg0140704)

摘　　要：《高等数学》和《数学分析》等教材,定义无穷限广义积分integral from n=-∞ to +∞ f(x)dx收敛条件是integral from n=-∞ to a 和integral from n=a to +∞ f(x)dx同时收敛,笔者通过分析、比较提出更合理的收敛定义,即integral from n=-∞ to +∞ f(x)dx的收敛条件只需lim A→+∞ integral from n=-A to A f(x)dx收敛即可.无界函数广义积分可得同样的结论.Some books like Advanced Mathematics and Mathematical Analysis etc. definite the condition of Astringency of Improper Integral is and astringe together. By analyzing and comparison, the penman brings forward a proper definition of Astringency, that is the condition of Astringency of only astringe by. The same as the Improper Integral of Unbounded Function.

关 键 词：广义积分 对比 收敛 合理性 

分 类 号：O17[理学—数学]