| 缔合勒让德函数的解析表达式研究 |
| |
| 引用本文： | 张捍卫,李明艳,雷伟伟.缔合勒让德函数的解析表达式研究[J].大地测量与地球动力学,2015,35(4):645-648. |
| |
| 作者姓名： | 张捍卫 李明艳 雷伟伟 |
| |
| 作者单位： | 1.河南理工大学测绘学院，焦作市世纪大道2001号,454003 |
| |
| 摘 要： | 把任意n阶m次缔合勒让德函数Pmn(cosθ)表示为系数E(k)与角度(n－2k)θ的正弦或余弦乘积之和，k的取值范围是0到int\n/2\]。当缔合勒让德函数的次小于等于2时，其系数E(k)可利用P0n(cosθ)展开式的系数来表示|否则，其将是几个数组的线性组合。本文给出的解析表达式有助于理解勒让德函数的特性及证明。
|
| 关 键 词： | 勒让德函数 缔合勒让德函数 三角函数 解析表达式 |
| 收稿时间： | 2014-07-18 |
Restudy on Analytical Expression of Associated Legendre Function |
| |
| ZHANG Hanwei,LI Mingyan,LEI Weiwei.Restudy on Analytical Expression of Associated Legendre Function[J].Journal of Geodesy and Geodynamics,2015,35(4):645-648. |
| |
| Authors: | ZHANG Hanwei LI Mingyan LEI Weiwei |
| |
| Institution: | 1.School of Surveying & Land Information Engineering, Henan Polytechnic University, 2001 Shiji Road, Jiaozuo 454003, China |
| |
| Abstract: | In this paper, the associated Legendre function, with arbitrary order n and degree m Pmn(cosθ), is represented as the product sum of the coefficient E(k) and the angle (n－2k)θ′ss sine or cosine. The available value range of k is from 0 to int\n/2\]. 〖JP2〗When the degree m is less than or equal to 2, E(k) can be expressed by the coefficient of P0n(cosθ) expansion. Otherwise, it will be a linear combination of several arrays. The given analytical expression not only helps to understand the Legendre function’s characteristics and property proof, but also can simplify its application in the related technical field. |
| |
| Keywords: | Legendre function associated Legendre function trigonometric function analytical expression |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
| 点击此处可从《大地测量与地球动力学》浏览原始摘要信息 |
| 点击此处可从《大地测量与地球动力学》下载免费的PDF全文 |
