半径

And the radius of convergence of the differentiated series is the same as for the orginal series.

逐项求导后所得到的幂级数和原级数有相同的收敛半径。

And the radius of the convergence set of the differentiated series is the same as for the orginal series.

定理5 如果幂级数的收敛半径为则其调和函数在内可导，且有逐项求导公式

Power series, radius of convergence; function that can be expanded in a power series on an interval.

幂级数；收敛半径；可展开为幂级数的函数。

The radius of convergence can be characterized by the following theorem

收敛半径可以被如下定理刻画

For example,we have the following simple result:Lei the Taylor series F =has a radius of convergence or 1, where 0 = If F is of order p (For the two cases of the radius of convergence,the meanings of "order"are different.).

如果这级数有级ρ(在收敛半径是∞或1时，"级"的意义不同)，那么在第一种情形。

Property 2 (Term-by-Term Integration) Suppose that is the sum of a power series on interval ;that is,Then, if is interior to ,and the radius of convergence of the integrated series is the same as for the orginal series.

性质 2 幂级数的和函数在其收敛域上可积，并有逐项积分公式，，逐项积分后所得到的幂级数和原级数有相同的收敛半径。

Therefore, to counter the possible problems to be met in the application, we study objectively the model structures, algorithms and capabilities for these neural networks, such as the quick learning of the multilayer feedforward network, the learning algorithm of increasing the storage capacity and the convergence radius of Hopfield network, the structure and mapping capability of the fuzzy inference network, the automatic learning of the fault diagnostic expert network and so on.

分别研究了多层前馈网络的快速训练问题、增大Hopfield网络存贮容量和收敛半径的学习算法、模糊推理网络的模型和映射能力，以及故障诊断专家网络知识的自学习问题等。

The radius of convergence of a power series ''f'' centered on a point '' a '' is equal to the distance from ''a'' to the nearest point where '' f '' cannot be defined in a way that makes it holomorphic.

一个中心为'' a ''的幂级数''f''的收敛半径'' R ''等于''a''与离'' a ''最近的使得函数不能用幂级数方式定义的点的距离。

The Pade approximation is combined with 3-D frequency-domain finite difference (3D-FDFD) for the first time. The impact of expansion point and the order of rational function on the accuracy and the convergence radius is discussed in this dissertation.

主要包括以下内容：首次将Pade逼近运用到三维频域有限差分法中，详细讨论了Pade逼近中展开点选取、收敛半径与有理阶数的关系问题。

The law of the influence of contractive angle of taper nozzles and curvature radius of convergence nozzles' convergent section on jet structure parameters is revealed, and it can provide a basis for optimization selection and design about laser cutting nozzles.

揭示锥型喷嘴收缩段收缩角、收敛型喷嘴收敛段抛物线曲率半径对射流的流场结构参数的影响规律，为激光切割喷嘴的优化选择和设计提供有效依据。标签激光技术激光切割会聚型喷嘴流场结构流体动力学 laser technigue laser cutting assemble nozzle jet structure hydrokinetics

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。