求和公式

The application problems mainly focus on how to solve triangle, acute triangle function, equation, inequation, function and its image, the three-dimensional image of a solid; while such knowledge as, plane geometry, solid geometry, operation of number and equation, trigonometric function equation, permutation and combination, ordered series of numbers sum, probability has no application problems.

4高中物理学习中存在运用困难的数学知识主要有函数及其图像、解三角形、锐角三角函数、方程、不等式、求函数极值、几何体的三视图等，然而，平面几何、立体几何知识、数与式的运算、三角函数公式、排列组合、数列求和、概率等知识基本没有运用困难。

In studying the linear response of the dressed quark propagator in the presence of the variable external field, we derive a general expression for the vacuum susceptibility, based on the two-point external field formula in the Quantum Chromodynamical sum rule. The expressions we have derived for the calculation of vacuum susceptibility are model independent. Then we use the expressions to calculate the renormalised axial vector, vector and tensor vacuum susceptibilities.

接下来在研究夸克传播子在外场中的线性响应时，我们利用QCD求和规则两点外场公式推导出了一般的计算真空磁化率的公式（以变化的轴矢量外场为例），我们这里推导出的真空磁化率的计算公式是模型无关的。

Based on the second-order moment of the power density, the far-field divergence angle of nonparaxial rotationally symmetric Laguerre-Gaussian beams is derived and expressed in a sum of the series of the Gamma function.

基于功率密度的二阶矩方法，推导出了非傍轴旋转对称拉盖尔－高斯光束远场发散角的解析公式，并表示为伽玛函数的幂级数求和形式。

This book reviews the many areas of numerical analysis, including the configuration polynomial, finite difference, factorial polynomials, summation, Newton formula, operator and configuration polynomial, Cheung section, close polynomials, TaylM more item type, interpolation, numerical differentiation, numerical integration, and with the series, differential equations, differential equations, least squares polynomial approximation, minimax polynomial approximation, rational function approximation, triangular approximation, non-linear algebra, linear equations, linear programming, boundary value problems, MonteCarIo methods and so on.

本书综述了数值分析领域的诸多内容，包括配置多项式、有限差分、阶乘多项式、求和法、Newton公式、算子与配置多项式、祥条、密切多项式、TaylM多项式、插值、数值微分、数值积分、和与级数、差分方程、微分方程、最小二乘多项式逼近、极小化极大多项式逼近、有理函数逼近、三角逼近、非线性代数、线性方程组、线性规划、边值问题、MonteCarIo方法等内容。本书的特色主要表现在利用例题及大量详细的题解来透彻地阐明所述内容的内涵，同时附有大量的补充题以便读者进一步巩固和深化从书中获得的数值分析知识。

Then, the boundary points are extracted. By using Shu's theorems the sum of Legendre polynomial of the boundary points is calculated.

首先使用Yang-离散格林公式将二值图像矩计算中区域内求和转换为沿区域边界求和；然后提取该图像的边界点；再利用Shu提出的公式计算出边界点的Legendre多项式的叠加值。

On the other hand, this paper introduces the idea of making the use of general formula or recurrence formula to resolve the summation problem and debugging the program on the blackboard.

另外，本文提出了利用通项公式或递推公式求和及在黑板上调试程序的思想。

The sum of the series, it is necessary to pay attention to the scope of application of the formula and the formula derived process, to observe the series of characteristics and laws.

对于数列的求和，要注意公式的应用范围和公式的推导过程，注意观察数列的特点和规律。

In other words, we are going to have to use the formulas given in the summation notation review to eliminate the actual summation and get a formula for this for a general n.

换句话说，我们要用求和符号来代替实际的求和，从而就能得出对于一般的n都适用的公式。

As we know, spiro-conjugated compound 1',3',3'-trimethyl-6-hydroxyspiro[2H-1-benzopyran-2,2'-indoline] is one of thesignificant photochromic species, the structure and spectrum ofthe compounds 1',3',3'-trimethyl-6- hydroxyspiro[2H-1-benzopyran-2,2'-indoline] and its isomers have studied.

三。研究了一类重要的光致变色物质之一螺旋共轭化合物1′，3′，3′-三甲基-6-羟基螺旋[2H-1-苯并吡喃-2，2'-二氢吲哚]及其光异构化产物的结构、光谱，并在此基础上，用完全态求和公式自编程序计算了非线性光学系数。

5 Involving four arbitrary sequences and other general bilateral summations.

并由此得到了几个基本超几何级数求和公式及其极限情况。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。