利用一致收敛求和式极限  

The Limit of Sum Form Obtained by Uniformly Convergent

作　　者：舒文豪 邝思颖 胡晓莉 SHU Wenhao;KUANG Siying;HU Xiaoli(School of Artificial Intelligence,Jianghan University,Wuhan 430056,Hubei,China)

机构地区：[1]江汉大学人工智能学院,湖北武汉430056

出　　处：《江汉大学学报（自然科学版）》2023年第4期29-35,共7页Journal of Jianghan University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11501251)。

摘　　要：和式极限是重要极限问题之一,在数学各分支领域有着广泛的应用。它复杂多样、灵活多变,通常没有固定的解题方法。一道关于函数列一致收敛性的考研题引发了笔者对函数列和式极限问题的思考。通过对和式极限进行适当的变形与整理,构造一致收敛函数,可以巧妙地解决一系列函数列和式极限问题。对所得结论给出了严谨的推理证明,为解决此类问题提供了一般性思路,并通过对典型例题的分析,从而更有利于初学者对此类问题的理解与把握。The limit of sum form is one of the most important limit problem and has a wide range of applications in all branches of mathematics.It is complex,diverse,and flexible,and there is usually no fixed method to solve it.A postgraduate examination question about the uniform convergence of function sequences triggered the author to think about the limit of sum form with function sequences.By deforming and arranging the limit of the sum form properly and constructing the uniform convergence function,a series of the limit of the sum form with function sequence problems can be solved skillfully.We give rigorous reasoning proof to the conclusion and provide general ideas for solving such problems.Through the analysis of typical examples,it is helpful for beginners to understand and grasp such problems.

关 键 词：一致收敛 和式极限 极限函数 

分 类 号：O171[理学—数学]