摘要
根据一致收敛与收敛的关系,得到一种判定含参量无穷限反常积分非一致收敛的方法.通过观察被积函数中的不定式,若能找到参量关于积分变量的函数,使得相应的无穷限反常积分发散,那么含参量无穷限反常积分非一致收敛.相对于定义法和柯西准则,该方法更加简便.
According to the relationship between uniform convergence and convergence, a judging method for non uniform convergence of improper integral with parameters was obtained. If some parameter is found to be the function of integral variable by observing the infinitives in integrand function such that the corresponding integral is divergent, then the improper integral with parameters convergent non-uniformly. The method is easier than definition method and the Cauchy criterion.
出处
《高师理科学刊》
2016年第1期15-19,共5页
Journal of Science of Teachers＇College and University
基金
国家级特色专业建设点项目(TS11575)
关键词
含参量无穷限反常积分
非一致收敛
不定式
发散
improper integral with parameters
non uniform convergence
infinitive： divergence
