形式幂级数

将双曲函数展开式作为特殊的形式幂级数，通过形式幂级数运算获得双曲类型4组孪生恒等式，其中3组与Bernoulli数、Euler数有关。

Taking the expansion of hyperbolic function as a special formal power series , through the hyperbolic operation of formal power series , the author obtains four groups of twin identity of hyperbolic type , among which three groups are related to Bernoulli 's numbers or Euler 's numbers .

本文将形式幂级数的概念作了推广，使之可以处理半因果性的离散信号，在此范围内，卷积逆和卷积幂的运算都可以无障碍地进行，形成了形式幂级数域。

In this paper , the " ring of formal power series " is extended to " field of formal power series ", which copes with " semi-causal sequences " and solves the problem of " convolution quotient " and " convolution power " totally within this scope .

形式幂级数域及广义Z变换在离散信号分析中的应用

On the field of formal power series and generalized Z transform with applications to discrete signal analysis

当指定Z为复数变元时，就有了形式幂级数的变换函数，即闭合形式的问题。

When Z is assigned the meaning of a complex variable , problem of " closed form " of formal power series emerges .

研究了随机形式幂级数的Pad啨逼近.证明了任意Pad啨逼近的a。

The Pad é approximation of stochastic power series is studied , and existence of arbitrary Pad é approximation is proved .

随后，通过变量代换，我们将本文所考虑的Cauchy问题的形式幂级数解转化为一个q-级数。

By variable substitutions , we can transfer the divergent formal solution to our Cauchy problem into a q-series .

形式幂级数半环的同态与同余

Homomorphism and Congruence on Semi - ring of Formal Power Series

形式幂级数方法在矩阵运算中的应用

The Method of Formal Power Series in Matrix Algebra

本文运用形式幂级数的技巧，证明了一个重要的组合恒等式。

In this paper , an important combinatorial identity is obtained by means of the formal power series .

我们把它应用到线性偏微分方程上去得到了解的规模和形式幂级数解。

We apply Wu-Ritt method to linear partial differential equations and gave the size of solution arid formal Taylor solutions .

关于偏微分方程解的规模，恰当解，形式幂级数解和序的优化

On the size of solution , proper solution , formal Taylor series solutions and the optimization of orderings for some PDEs

即如果方程各项中“秩”的取值全为奇数或偶数，则可借助椭圆方程的方法解之；若方程各项中“秩”的取值奇偶性不一致，则给出一形式幂级数解。

In other words , we can solve them with the aid of the elliptic equation when " rank " values of every term in equations are odd or even .

该文利用自由幺半群上的有理形式幂级数理论，构造出该概率分布的约化线性表示，从而完全解决了噪声变量的概率分布计算问题。

In this paper , we propose a reduced linear representation of such distribution based on the formal power series on free monoid which can be easily used to calculate the probability distribution .

裂纹尖端附近的应力和位移被表达为解析复函数的形式，而复函数可以表达为幂级数的形式，幂级数的系数由研究问题的边界条件来确定。

The stresses and displacements near the crack tip are expressed as analytical complex functions , which can be represented in power series . The constant coefficients of the series are determined with boundary conditions .