级数求和

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。

A new method of gravity gradient vector field for quantitative determination of field source is described in this paper.

本文叙述了利用重力梯度矢量场确定场源的一种新方法，采用富里哀级数求和的算法。

An S-shape acceleration/deceleration control model is developed by summation progression and the corner of two conjoint lines is adopted as a parametric variable to control the feedrate through the inflexion of two lines. Based on these, interpolation process is divided into two steps: interpolation pretreatment and interpolation point calculation. Feedrate planning is accomplished in the pretreatment step. Interpolation point calculating only depends on the real-time feedrate and the direction vector of the line.

该算法以级数求和的方法推导了S型加减速控制模型，并以小线段夹角为参变量控制拐点通过速度建立了小线段速度衔接模型，在此基础上，算法将插补过程分解为插补预处理及插补点计算两个步骤，预处理中对小线段进行速度规划并设计了线段速度的递推处理方法，插补点仅需根据当前速度及线段方向向量即可求出。

Summation of infinite series is part of the process of learning more difficult to grasp the progression part, this article summarizes the common summation of several infinite series method, as has the use of progression and the definition of sum, the use of itemized points or one differential sum, the use of split-phase elimination method of summation methods, and problem-solving steps in detail.

无穷级数的求和部分是学生学习级数过程中较难掌握的部分，本文归纳了常见的几种无穷级数的求和方法，像有利用级数和的定义求和、利用逐项积分或逐项微分法求和、利用裂项相消法求和等方法，并提出了详细的解题步骤。

For example, geometric series can be used to evaluate the sum of power series and can be used to determine the convergence of other series.

例如可以用几何级数来解决幂级数的求和问题、以及用它作为优级数来判定其他级数的收敛性等等。

From three respects in calculus teaching, this paper has mainly discussed magical effect of physics meaning of questions, which is curve integration curved surface integration and sum of series formula.

微积分的教学离不开问题的物理意义，文章从曲线积分、曲面积分以及级数求和公式的推导等三个方面来说明问题的物理意义在微积分教学中的妙用。

Via generalizing the Cauchy method we obtain a new method,called the modified Cauchy method.By means of this method we establish two bilateral _3ψ_3 and _4ψ_4 series summation formulae,two four-term summation and transformation formulae for unilateral _3φ_2-series and bilateral _3ψ_3-series,and two five-term summation and transformation formulae for unilateral _3φ_2-series and bilateral _3φ_3-series,which contain many known results as their special cases,such as non-terminating q-Saalschütz summation formula,Bilateral _6ψ_6 series summation formula of Bailey,non-terminating Watson transformation formula and some transformations of _3φ_2-series etc.

通过对Cauchy方法的推广，我们得到修正的Cauchy方法，采用这个方法分别得到两个双边的_3ψ_3和_4ψ_4基本超几何级数的求和公式、单边_3φ_~(2-)级数和双边_3ψ_(3~-)级数的两个四项求和变换公式和两个五项求和变换公式，它们包括许多已有的结果为特例，如非终止的q-Saalschütz求和公式、Bailey的very-well-poised双边级数_6ψ_6求和公式、非终止的Watson变换公式和一些关于单边_3φ_(2~-)级数的变换公式等。

Computation result is compared with the direct summation of the series form solutions of the electromagnetic filed over the sphere.

同球外电磁场直接级数求和表达式的计算结果进行了比较。

The biggest advantage of this mean is that don"t need to computer the perturbation matrix element by using zero level wave function, even don"t need to give out high rank amendatory result using infinite series to sum like the ordinary perturbation theory. Thus, it not only avoids many complicated integral operation, but also obtains high rank amendatory result that it is very difficult to get or cant get.

这种方法最大的优点就是不需要用零级波函数来计算微扰矩阵元，更不需要像普通微扰论那样用无穷级数求和给出高阶修正的结果，这样一来，不仅避免了许多繁复的积分运算，而且求得了普通微扰论很难得到或不可能得到的高阶修正的结果。

Based on the author's own teaching accumulation , this paper puts forward kinds of summations of power series and series of numbers through exmaples .

结合自己的教学积累，通过实例，给出数项级数求和的多种途径。

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。