对广义罗尔定理进行了证明，并应用广义罗尔定理讨论了勒让德多项式的零点。
This paper demonstrates the generalized Rolle theorem and discussed the zero of Legendre polynomials.
通过实例分析，探讨用勒让德多项式和定解条件求解静电场时确定系数的方法。
By analyzing the sample, study the method of seeking given parameters by using Lengendre polynomials and condition of fixed solution.
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.
根据计算精度要求，确定福里哀级数和勒让德多项式的项数，从而得到实用简化公式。
According to the desired accuracy, we determine the number of terms in the Fourier series and Legendre polynomials, then the Practical simplified formulae are obtained.
应用勒让德多项式的加法定理和类似于求傅里叶系数的方法，导出了新展式中系数的普遍表达式。
The method, which we use to derive the general expressions for the new coefficients in the development of gravity anomaly Ag(m, a), is analogous to Fourier's.
分析了几种经典的滤波器原型设计原理及其自身不足，基于勒让德多项式，给出了一种新的低通滤波器设计原型。
Based on Legendre multinomial, a new kind of low-pass filter prototype is designed out after analyzing the design rule and inefficiency of some classical filter prototypes.
一般多项式都可以展开为正交多项式的级数形式，而勒让德多项式、厄米特多项式和拉盖尔多项式都是典型的正交多项式。
All ordinary polynomials have series expansion of orthogonal polynomials, while Legendre polynomials, Hermite polynomials and Laguerre polynomials are special orthogonal polynomials.
一般多项式都可以展开为正交多项式的级数形式，而勒让德多项式、厄米特多项式和拉盖尔多项式都是典型的正交多项式。
All ordinary polynomials have series expansion of orthogonal polynomials, while Legendre polynomials, Hermite polynomials and Laguerre polynomials are special orthogonal polynomials.
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