| δ函数的导函数的Legendre非线性逼近 |
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| 引用本文： | 潘云兰.δ函数的导函数的Legendre非线性逼近[J].浙江师范大学学报(自然科学版),2006,29(4):373-377. |
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| 作者姓名： | 潘云兰 |
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| 作者单位： | 浙江师范大学,数理与信息工程学院,浙江,金华,321004 |
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| 基金项目： | 浙江省留学回国人员基金;浙江省教育厅资助项目 |
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| 摘 要： | 讨论了利用变形Legendre多项式母函数的非线性逼近.当这类非线性逼近应用于D iracδ函数的导函数时,它们被证明是Gauss求积公式应用于这一导函数的含有前述母函数的Stieltjes积分表示式.进一步证得了收敛性,导出了逼近误差.
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| 关 键 词： | 非线性逼近 母函数方法 Diracδ函数的导函数 Legendre多项式 |
| 文章编号： | 1001-5051（2006）04-0373-05 |
| 收稿时间： | 2006-06-05 |
| 修稿时间： | 2006-09-05 |
Legendre nonlinear approximations to the derivative of delta function |
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| PAN Yunlan.Legendre nonlinear approximations to the derivative of delta function[J].Journal of Zhejiang Normal University Natural Sciences,2006,29(4):373-377. |
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| Authors: | PAN Yunlan |
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| Institution: | College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua Zhejiang 321004, China |
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| Abstract: | The nonlinear approximations based on the modified generating functions of the Legendre polynomials were studied.It was showed that such nonlinear approximations to the derivative of Dirac delta function on() were the corresponding Gaussian quadratures applied to its Stieltjes integral representations,whose integrands contain weights and the modified generating functions of Legendre polynomials.In addition,the convergence was proved and the error term was presented. |
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| Keywords: | nonlinear approximation generating function method derivative of Dirac delta function Legendre polynomial |
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