函數(shù)項(xiàng)級(jí)數(shù)一致收斂的判別-展示頁
2025-05-25 02:04本頁面
【正文】 函數(shù)項(xiàng)級(jí)數(shù)一致收斂的判別摘 要：函數(shù)項(xiàng)級(jí)數(shù)的一致收斂性是函數(shù)級(jí)數(shù)概念當(dāng)中最基本最重要的問題。 本文則在數(shù)項(xiàng)級(jí)數(shù)的基礎(chǔ)上, 分析函數(shù)項(xiàng)級(jí)數(shù)的收斂性定義及其判定, 函數(shù)項(xiàng)級(jí)數(shù)的分析性質(zhì)和函數(shù)的一致收斂有關(guān)。本文對(duì)函數(shù)項(xiàng)級(jí)數(shù)一致收斂的判別法進(jìn)行推廣, 主要?dú)w納總結(jié)出了對(duì)數(shù)判別法, 導(dǎo)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(shí)并應(yīng)用函數(shù)項(xiàng)級(jí)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。 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 discrimination law, and apply function series consistent definition of convergence, it is important discrimination method and the necessary and sufficient conditions are given some proof of the conclusion of the paper.Keywords: Function Series。 discrimination law.前 言 一致收斂性是函數(shù)項(xiàng)級(jí)數(shù)的一個(gè)重要性質(zhì), 有效地判別函數(shù)項(xiàng)級(jí)數(shù)的一致收斂對(duì)進(jìn)一步研究函數(shù)項(xiàng)級(jí)數(shù)的性質(zhì)起著重要的作用。 而本文在給出這些判別法的同時(shí)并對(duì)函數(shù)項(xiàng)級(jí)數(shù)一致收斂的定義，柯西判別法，M判別法，阿貝爾判別法，萊布尼茲判別法加以補(bǔ)充和推廣，從而給判別函數(shù)項(xiàng)級(jí)數(shù)一致收斂提供了方便。對(duì)于函數(shù)項(xiàng)級(jí)數(shù), 我們不僅要討論它在哪些點(diǎn)上收斂,
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