| 关于一类椭圆积分的化简 |
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| 引用本文： | 石永芳,雷鸣宇,雷桂林.关于一类椭圆积分的化简[J].海南大学学报(自然科学版),2014(1):8-11. |
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| 作者姓名： | 石永芳 雷鸣宇 雷桂林 |
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| 作者单位： | [1]兰州文理学院师范学院,甘肃兰州730000; [2]中国移动北京公司,北京100007; [3]兰州文理学院电子信息工程学院,甘肃兰州730000 |
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| 摘 要： | 将正椭圆锥的立体角化为斜椭圆锥的立体角,从而用椭圆积分Ⅰ,Ⅱ表示立体角,通过积分法求出了正椭圆锥的立体角,得到了用椭圆积分Ⅲ表示的立体角.由于2种方法表示的立体角相等,可将一类椭圆积分Ⅲ化成了椭圆积分Ⅰ,Ⅱ的形式.
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| 关 键 词： | 斜圆锥 正椭圆锥 立体角 椭圆积分 |
Simplification of a Class of Elliptic Integral |
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| Institution: | SHI Yong-fang , LEI Min-yu, LEI Gui-lin(1 Sehool of Teachers, Lanzhou University of Arts and Science, Lanzhou 730000, China; 2. China Mobile Beijing Company, Beijing 100007, China; 3. School of Science and Engineering Colleges, Lanzhou University of Arts and Science, Lanzhou 730000 ,China) |
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| Abstract: | In our report, the solid angle of normal elliptical cone was transformed to an oblique cone＇ s solid an- gle, and which was expressed by elliptic integrals Ⅰ and Ⅱ , respectively. The integration method was used to obtain the solid angle of normal elliptical cone, and which was expressed by elliptic integral Ⅱ. Because the sol- id angles which are expressed by the two kind way were same, it was feasible to transform a kind of elliptic inte- gral Ⅲ into elliptic integrals Ⅰ and Ⅱ. |
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| Keywords: | oblique cone normal elliptical cone solid angle elliptic integral |
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