The dual symmetry of Legendre transformation is studied.

指出热力学关系具有勒让德变换的对偶对称性。

Diophantine equation; prime; integer solution; Legendre symbol; congruence.

丢番图方程；素数；整数解；勒让德符号；同余。

"France symbolises a cultural wonder, industrial know-how, the good life," said architect Legendre.

“法国象征文化奇迹、工业强国、美好生活，”建筑师勒让德说。

This paper demonstrates the generalized Rolle theorem and discussed the zero of Legendre polynomials.

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。

The problem of rapid Lunar soft-landing trajectory optimization by using a Legendre pseudospectral method was studied in this paper.

研究了伪光谱方法在空间飞行器有限推力轨道转移最优化问题中的应用。

The angular coordinate used a DVR based on Legendre polynomials and the radial coordinates utilized a DVR based on sine basis functions.

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 higher-order hierarchical Legendre basis functions based MOM is introduced, and the AIM is employed to accelerate the solving procedure.

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 numerical results exhibit a great saving in the computational efforts for the proposed integration scheme as compared with the Gauss-Legendre one.

数值结果显示所提出的积分方案在计算效率上比高斯-勒让德积分有大幅度提高。

For high quality voice transformation, a novel parameter extraction scheme for glottal flow derivative is proposed based on Legendre orthogonal decomposition.

提出了一种用于源-目标说话人声门波导数参数转换的、基于勒让德正交分解的声门波导数波形参数提取方法。

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.

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。

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.

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。

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.

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。

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。

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.

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。