介绍勒让德方程在自然边界条件下的解，重点推导了勒让德函数的系数。
The solution of Legendre equation has been introduced in the condition of natural limit and the emphasis is put on the inference to the coefficient of the Legendre function.
文中运用了一种改进的球谐函数法，即换极法，大大简化了勒让德函数的递推计算，并进行了换极前后被动段扰动引力的仿真计算。
In this paper the improved method, also named transformation of the polar, is used to predigest the iterative calculation, and the simulation calculation has been progressed.
本文研究了散射相函数的有限项的勒让德展开对于求解辐射传输方程的误差效应，提出了一个改进算法。
In this paper, the effect of Legendre expansion of scattering phase function with a finite number of terms on solving radiative transfer equation is studied and an improved algorithm suggested.
文章给出了基于高阶叠层型勒让德基函数的矩量法公式，并引入自适应积分方法来加速其求解过程。
The higher-order hierarchical Legendre basis functions based MOM is introduced, and the AIM is employed to accelerate the solving procedure.
角度部分的DVR基组选择勒让德多项式形式，而径向坐标采用正弦函数形式。
The angular coordinate used a DVR based on Legendre polynomials and the radial coordinates utilized a DVR based on sine basis functions.
针对勒让德谱元方法，构造了一类混合局部基函数，并证明了其线性无关特点。
A class of hybrid basis are designed for Legengre spectral element method and it's linear independence is proved.
针对勒让德谱元方法，构造了一类混合局部基函数，并证明了其线性无关特点。
A class of hybrid basis are designed for Legengre spectral element method and it's linear independence is proved.
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