| 幂级数在收敛区间端点收敛时的性质 |
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| 引用本文： | 刘小川,何美.幂级数在收敛区间端点收敛时的性质[J].数学学习,2011(3):19-20,36. |
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| 作者姓名： | 刘小川 何美 |
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| 作者单位： | 山西大同大学数学与计算机科学学院,山西大同037009 |
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| 摘 要： | 讨论幂级数及其逐项积分、逐项求导后的级数在收敛区间端点收敛时的若干性质,给出它们之间敛散性的关系,并把连续性和逐项可积性推广到幂级数的收敛域上.
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| 关 键 词： | 幂级数 一致收敛 逐项积分 逐项求导 |
Power Series at the Endpoints of Its Interval of Convergence |
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| LIU Xiao-chuan,HE Mei.Power Series at the Endpoints of Its Interval of Convergence[J].Studies In College Mathematics,2011(3):19-20,36. |
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| Authors: | LIU Xiao-chuan HE Mei |
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| Institution: | (School of Mathematic and Computer Science, Shanxi Datong University, Datong 037009, PRC) |
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| Abstract: | Some properties of a power series at the endpoints of its interval of convergence are discussed. Relations of the endpoints convergences between the power series, its derivative or integration （in the sense of term-by-term） are also investigated. The continuity of a power series and the eligibility of the term-by-term integration are generalized to the domain of convergence. |
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| Keywords: | power series uniformly convergent term-by-term integration term-by-term derivative |
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