函數(shù)項級數(shù)一致收斂的判別(已修改)
2025-05-28 02:04 本頁面
【正文】 河南師范大學新聯(lián)學院本科畢業(yè)論文 學號：0901174099函數(shù)項級數(shù)一致收斂的判別專業(yè)名稱： 數(shù)學與應用數(shù)學 年級班別： 2009級1班 姓 名： 張慶明 指導教師： 左紅亮 2013年04月 河南師范大學新聯(lián)學院本科畢業(yè)論文 函數(shù)項級數(shù)一致收斂的判別摘 要：函數(shù)項級數(shù)的一致收斂性是函數(shù)級數(shù)概念當中最基本最重要的問題。 本文則在數(shù)項級數(shù)的基礎上, 分析函數(shù)項級數(shù)的收斂性定義及其判定, 函數(shù)項級數(shù)的分析性質(zhì)和函數(shù)的一致收斂有關。而因此本論文中提出了函數(shù)級數(shù)一致收斂的定義, 柯西一致收斂準則, 魏爾斯特拉斯判別法(M判別法), 狄利克雷判別法, 阿貝爾判別法, 余項判別法, 積分判別法。本文對函數(shù)項級數(shù)一致收斂的判別法進行推廣, 主要歸納總結(jié)出了對數(shù)判別法, 導數(shù)判別法, 連續(xù)性判別法, 逼斂性判別法以及M判別法的推論等幾種判別法, 同時并應用函數(shù)項級數(shù)一致斂的定義, 重要判別法及其充要條件給出了論文中一些結(jié)論的證明。關鍵詞：函數(shù)項級數(shù)；一致收斂性；判別法。 Discrimination of uniform convergence of function seriesAbstract: The uniform convergence of function series is the concept of series of functions are the most basic and most important problem. In this paper, on the basis of a number of series, the definitions of convergence of function series and its decision, uniform convergence analysis of properties and functions related to the function of series. Therefore, this paper proposes a definition of uniform convergence of function series, Cauchy uniform convergence criteria the Weierstrass discrimination method (M identification method), Dirichlet discrimination law, Abel discriminant law, the remainder discriminant method, integration criterion method and article on the function series convergence discriminant method to promote mainly summarized Diagnostic Method derivative test, continuity discrimination law, forcing several discriminant method of convergence discrimination law and M inference of
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