求幂级数收敛域最关键的是求它的收敛半径。
To find the solution of power series convergence domain, it is important to get its radius of convergence.
为了克服级数收敛缓慢的缺点，提出级数求和公式。
In order to overcome the demerit of the slowness of the series convergence, we put forward the series summation formula.
在规定的范围内该无穷级数收敛，并有计算公式成立。
Within the restricted scope, the infinite power series is convergent and the formula is workable.
比式判别法和根式判别法是对正项级数收敛性进行判别的两种广用的方法。
The ratio test and the root test are two widely used convergence tests for positive series.
着重讨论了远洋区的实施方案，导出了必要的工作公式，并就加速远洋区级数收敛问题作了探讨。
We pay treat attention to the working plan for the far. ocean area. Calculated formulas and coefficients concerned are given, and the problem to speed up the convergence of series is studied.
文章通过对无穷小量与无穷大量的阶的概念研究，用阶的估计讨论数学分析中数列、函数及级数收敛问题，也为收敛问题深入研究提供了一种方法。
This paper studies the concept of infinitesimal and infinity, and discusses the convergence of sequence, function and series with the estimation of the orders.
该级数一致收敛于收敛环内的紧子集上。
The series converges uniformly on compact subsets of the interior of the annulus of convergence.
无穷级数的收敛性与发散性与此概念有关。
Convergence and divergence of infinite series depend upon this concept.
适当选取参数，得出了几个新的收敛级数。
By choosing suitable parameters, several new and convergent series are obtained.
它们有相同的收敛区间，应用代入法求出它们的级数和，从而获得孪生组合恒等式。
Because they have same convergence region, sum of series and combinational twin identifies was obtained using the method of substitution.
要准确计及电子相关效应，还需通过作更高阶展开，以考察级数的收敛性。
To estimate more accurately the electron correlation effects, one has to calculate to higher orders and check he convergency of the series.
第二部分是在一致收敛条件下函数列、函数项级数以及含参量反常积分的性质。
The second part is in uniform convergence conditions function series, function and parameter improper integral. We properties.
通过对阿贝尔定理的深入探讨，获得了幕级数在其收敛区间端点收敛的一些判别条件。
We obtain a sufficient condition and a essential - sufficient condition about convergence at the end point of the convergence interval of power series.
首先，通过对再生核的研究，给出了小波级数的部分和在跳跃间断点处的收敛性与再生核之间的关系的等价命题。
First, by studying the producing kernel, equivalent positions of the relation between the convergence of partial sums of wavelet expansions at jumping points and producing kernel are given.
讨论和分析了一类交错级数的收敛问题，给出了异于莱布尼兹判别法的关于交错级数的一个收敛定理。
We obtain a convergence theorem of alternative series differing from Leibniz test by discussing and analyzing the convergence of a kind of alternative series, and generalize the using limits of J.
并提出了一种基于几何级数的极限条件估计学习控制过程收敛条件的理论方法。
A theoretical consideration to estimate the convergence conditions in learning control process is proposed in accordance with the limit condition of a geometric series.
在建立积分方程时，运用平面高斯定理改善了级数的收敛性。
In deriving the integral equation, the convergence of series is modified by application of the plane Gauss Theorem.
用代数动力学方法求得了用泰勒级数表示的局域收敛的常微分方程的精确解。
By algebraic dynamical method, the exact analytical solutions of the ordinary differential equations are obtained in terms of Taylor series with local convergent radius.
仿真实验结果证明了改进演化算法对于实现函数级数字组合逻辑电路的硬件演化是可行的，并且提高了演化算法的演化效率和收敛性能。
The results of simulation prove that the improved algorithms are feasible for evolving the digital combinational logic circuits and improve the evolvable efficiency and convergence performance.
本文利用矩阵方法对二重函数项级数进行讨论，得到了极其自然的收敛条件。
In this paper double series of functions with posititve coefficients are discussed and a natural condition of the convergence is obtained with the aid of matrix methods.
通过对级数解的数值计算发现傅立叶准则和毕渥准则对级数解的收敛速度有显著的影响。
It is found that the Fourier and Blot Numbers have big effect on the convergence speed of series solution.
考虑非齐次波动方程初边值问题的形式级数解的收敛性问题。
The convergence of the formal series solution to the initial boundary value problem for the non-homogeneous wave equation is considered.
对于函数级数，研究其和函数的解析性质很重要，但函数级数必须具有一致收敛性，而判断函数级数的一致收敛性往往是比较困难的。
However, this study should be based on the fact that the series must have consistent convergence, the judgment of which is rather difficult.
这个收敛很慢的级数是莱布尼茨在1674年得到的。
This very slowly converging series was known to Leibniz in 1674.
用一个收敛很快的级数构造了非圆截面、线性电流分布环形等离子体的磁流体平衡解。
The MHD equilibrium solutions of a toroidal plasma with non-circular cross-section and linear current distribution are written in terms of a fast convergent series.
提出了一种基于几何级数的极限条件估计学习控制过程收敛条件的方法。
A theoretical method which estimates the convergence condition of the learning control process based o...
用比较直接的方法证明幂级数的和函数在收敛域内可以逐项微分的公式；并得到了计算傅立叶系数的一种简便方法。
A relatively direct method is expounded in this paper to prove the termwise differentiation of power series, and a simple method is expressed to calculate the Fourier coefficient.
性质3在级数中去掉、加上或改变有限项，不会改变级数的收敛性。
Property 3 Deleting, adding and altering the finite terms of the infinite series keep the convergence of the series.
性质3在级数中去掉、加上或改变有限项，不会改变级数的收敛性。
Property 3 Deleting, adding and altering the finite terms of the infinite series keep the convergence of the series.
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