函數(shù)項(xiàng)級數(shù)的一致收斂性及其應(yīng)用(已修改)
2025-06-30 23:47 本頁面
【正文】 函數(shù)項(xiàng)級數(shù)的一致收斂性及其應(yīng)用摘要：隨著科學(xué)技術(shù)的發(fā)展，隨著人們對級數(shù)的深入研究，,函數(shù)項(xiàng)級數(shù)的一致收斂性在應(yīng)用中起著至關(guān)重要的作用,，對函數(shù)項(xiàng)級數(shù)一致收斂性的判定方法進(jìn)行梳理、歸納，并舉例說明，以一類最簡單的函數(shù)項(xiàng)級數(shù)冪級數(shù)為例，說明函數(shù)項(xiàng)級數(shù)在計(jì)算方面的應(yīng)用.關(guān)鍵詞：函數(shù)項(xiàng)級數(shù)；一致收斂；冪級數(shù)Uniformly Convergence Series of Functions and ApplicationAbstract: With the development of science and technology, elementary function has failed to meet the needs of the people. Since the Cauchy gives the definition of infinite series, the theory of series has been developed rapidly with the indepth study of it. With the infinite series, series of functions came into being. Series of functions has a wide application in mathematics and engineering science. The uniformly convergence of series of functions plays an important role in application. During the application, the uniformly convergence of series of function and its judgment bee important. This article describes the concept of the uniformly convergence of series of functions, to sum up the judgment of the uniformly convergence of series of functions. We give many examples and take the series of powers to illustrate the application in calculation of series of functions.Key words: series of functions。 uniformly convergence。 series of powers目 錄1 引言……………………………………………………………………………………………………12 函數(shù)項(xiàng)級數(shù)的相關(guān)概念介紹…………………………………………………………………………2 函數(shù)列及其一致收斂性………………………………………………………………………2 函數(shù)項(xiàng)級數(shù)及其一致收斂性…………………………………………………………………3 一致收斂函數(shù)項(xiàng)級數(shù)的性質(zhì)…………………………………………………………………43 函數(shù)項(xiàng)級數(shù)的一致收斂性判別法……………………………………………………………………5 一般判別法……………………………………………………………………………………5 魏爾斯特拉斯判別法…………………………………………………………………………7 阿貝爾判別法與狄利克雷判別法……………………………………………………………7 阿貝爾判別法……………………………………………………………………… 8 狄利克雷判別法…………………………………………………………………… 8 類似數(shù)項(xiàng)級數(shù)判別法的函數(shù)項(xiàng)級數(shù)一致收斂判別法…………………………………… 10 比式判別法…………………………………………………………………………10 根式判別法…………………………………………………………………………11 對數(shù)判別法…………………………………………………………………………12 Dini判別法…………………………………………………………………………………134 冪級數(shù)的應(yīng)用……………………………………………………………………………………… 14 冪級數(shù)的定義……………………………………………………………………………… 14 冪級數(shù)的應(yīng)用……………………………………………………………………………… 14 冪級數(shù)在近似計(jì)算中的應(yīng)用………………………………………………………14 冪級數(shù)在計(jì)算積分中的應(yīng)用………………………………………………………15 冪級數(shù)在求極限中的應(yīng)用………………………………………………………
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