| 椭圆积分的一种新型计算法 |
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| 引用本文： | 苏耘,王春红.椭圆积分的一种新型计算法[J].长春大学学报,1999,9(3):17-18,22. |
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| 作者姓名： | 苏耘 王春红 |
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| 作者单位： | 空军长春飞行学院!长春130022 |
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| 摘 要： | 首先通过推导单摆振动周期公式以及计算椭圆的弧长，介绍了椭圆积分的由来，并给出第一类、第二类椭圆积分的一般表达式；然后利用蹇级数展开方法将被积函数表示为级数的形式；再经过简单的积分计算将椭圆积分表示为级数；最后通过一简单的程序，利用微计算出积分值。
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| 关 键 词： | 椭圆积分 幂级数 级数表示法 计算 单摆振动 |
A new method for calculating ellipse integral |
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| SU Yun WANG Chun hong Changchun Flying College Of Air Force,Changchun.A new method for calculating ellipse integral[J].Journal of Changchun University,1999,9(3):17-18,22. |
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| Authors: | SU Yun WANG Chun hong Changchun Flying College Of Air Force Changchun |
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| Institution: | SU Yun WANG Chun hong Changchun Flying College Of Air Force,Changchun 130022 |
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| Abstract: | This paper first introduces the origin of the ellipse integral by deriving the formula of the vibrating period of a simple pendulum and computing the arc length of an ellipse,and gives the general expressions of the first kind and the second kind of ellipse integral.By using power series expansion method,the integrand is expressed as the form of a series,and then the ellipse integral is expressed as a series through simple integration.Finally,the integral value is calculated through a simple programme with a computer. |
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| Keywords: | ellipse integral power series calculating with a computer |
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