| 幂级数和函数的解法综述 |
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| 引用本文： | 徐凤林,张秀丽.幂级数和函数的解法综述[J].山东轻工业学院学报,2006,20(1):94-98. |
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| 作者姓名： | 徐凤林 张秀丽 |
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| 作者单位： | 山东轻工业学院数理学院,山东济南250100 |
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| 摘 要： | 本文总结了求幂级数和函数的四种方法。一种方法是将待求级数分解成己知和函数的级数的运算（一般是加减）表达形式,然后逐一求和新的级数;第二种方法是“先求导,再积分”或“先积分,再求导”;第三种方法是把待求级数用基本初等函数的幂级数展开式表示出来;第四种方法是列写出和函数满足的微分方程,解此微分方程得到和函数。
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| 关 键 词： | 函数项级数 幂级数 和函数 |
| 文章编号： | 1004-4280（2006）01-0094-05 |
| 收稿时间： | 2005-12-26 |
| 修稿时间： | 2005年12月26 |
A survey of solutions of sum functions of power series |
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| XU Feng-lin,ZHANG Xiu-li.A survey of solutions of sum functions of power series[J].Journal of Shandong Institute of Light Industry(Natural Science Edition),2006,20(1):94-98. |
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| Authors: | XU Feng-lin ZHANG Xiu-li |
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| Abstract: | This paper summarizes some kinds of solutions of sum functions of power series.(1) The first sdution is to let series be decomposed into operative expression of function series whose sum functions are known;(2)"The second solution is the method of first derivation,second quadrature" or "first quadrature,second derivation";(3)The third one is to let series be expressed by basic elementary function's power series expansion;(4)The fourth one is to determine differential equations which sum functions satisfy,then solve the differential equations. |
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| Keywords: | series of functions power series sum functions |
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