收敛级数

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 .

应用三个绝对收敛级数相乘法解非圆形洞室的外域映射函数

Determination of the mapping function for the exterior domain of a non-circular opening by means of the multiplication of three absolutely convergent series

从微分方程的角度出发，分三个方面讨论了一类收敛级数求和问题的具体解法。

Summation of restrain progression is discussed from the perspective of the differential equation in three aspects .

本文证得（1）若λ具有弱滑脊性，那么λ-数乘收敛级数具有对偶不变性。

In this paper , the main results are : ( 1 ) If λ has the weak gliding hump property , then λ - multiplier convergent series has the dual-invariant .

改进和推广了Kadecˇ凸性模定理，并讨论了凸性模对无条件收敛级数和算子级数的应用。

Some results improve and generalize the Kade 's theorem on modulus of convexity , on the other hand , some applications of modulus of convexity to unconditionally convergent series and series of operators are given .

本文根据残数理论，给出两类收敛级数求和的一种简单方法，并给出了该方法的理论证明。

It is suggested that a simple method , based on the residue theory , can be used for the summation of two kinds of convergent series , the theoretical proof of the method is also given .

用阿贝尔求和法求出发散级数的广义和，跨出了求和由收敛级数到发散级数的一步.加速级数收敛的一种外推算法

In particular , by applying Abel summation method to obtain broad sense sum of divergence series , the calulation of summation was made from convergence series to divergence series . An Extrapolation Methed Used to Accelerate Convergence Series

关于收敛P级数的一般估值不等式

General estimation inequalities on the convergent p - series

证明了Fuzzy实直线上的绝对收敛的级数经过重排后其和不变。

It is proved that the the infinite sum of the absolute convergent series in the Fuzzy real line does not change after rearrangement , so generalize the corresponding result in analysis .

本文讨论了一类函数方程的一致收敛的级数解，并将结果用于术解三阶线性双曲型方程的边值问题。

In this paper the author discusses the uniform convergent series solutions to a class of the functional equations , and uses the result to solve the boundary value problem of linear equations of the third order .

本文应用广义函数的Fourrier积分变换导出了双参数地基上板弯曲问题的基本解，并将基本解展成一致收敛的级数形式。

By means of Fourier integral transformation of generalized function , the fundamental solution for the bending problem of plates on two-parameter foundation is derived in this paper , and the fundamental solution is expanded into a uniformly convergent series .

收敛正项级数余项rn的最优估计

Optimal Estimation of Remainder r_n in Positive Convergent Series

在左半平面收敛的Dirichlet级数与随机Dirichlet级数的下级与准确下级

Lower order and proximate lower order of Dirichlet setries and random Dirichlet setries convergent on left half plane

本文研究了二阶线性递归序列｛wn｝n∈z的倒数和的对称性，并且得出了关于｛wn｝n∈z的二个收敛的无穷级数，推广I。

In this paper we study the symmetry property of reciprocals sums of 2 order linear recursive sequences , and determine two infinite series involving 2 order linear recursive sequences is convergent .

本文阐明Fibonacci序列递推公式的三种证法，数学归纳法、试探法、母函数法（作一收敛的幂级数，作为母函数）。

This paper illuminates three kinds of prove of the recurrence formula of Fibonacci sequence , that is 1 : Mathematical induction method 2 : Probing method . 3 : The parent function method ( make a convergent series , and let it be the parent function ) .

既发散又收敛的无穷级数

Infinite series with divergence and convergence

利用级数的收敛准则讨论级数敛散性时，常用到等式与不等式的变换。

It is a routine method to use equalities and inequalities in discussing series convergence and divergence .

应用级数的收敛条件，级数计算误差小于0.51%。

Applying the converging condition of series , the error of series calculation is less than 0.51 % .

计算得到的光谱项表示为一个快速收敛的交错级数，与文献数据比较，结果令人满意。

The spectroscopic terms are fitted as a staggered progression with fast convergence , the spectrum constants were compared with the experimental data and the results are acceptable .

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 .

引入了Fuzzy级数的绝对收敛及Fuzzy幂级数等概念；

The concepts of absolute convergence of fuzzy series and fuzzy power series are introduced .

在Hilbert空间与可分Banach空间，用独立随机元收敛准则或三级数定理的思想，证明了关于随机级数的收缩原理

By the criteria of convergence about independent random vectors or that of three series , we prove the contraction principle about random series in Hilbert space and separable Banach space

对于在左半平面σ<0内收敛的下侧Dirichlet级数所定义的解析函数f1（s）定义了下级；

The defined lower order of analytic function f 1 ( s ) defined by lower side Dirichlet series convergent on the left half plane σ < 0 ;

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 in1674 .

非一致收敛的函数项级数

Non - uniformly Convergent Series With Function Terms

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 .

在阻抗边界条件下，地球表面上电或磁偶极子的赫兹位函数被表达成偶极源的直达波、镜像源的反射波与一绝对收敛的贝塞尔函数级数之和的解析形式。

Subject to impedance boundary condition , Hertz potentials of electric or magnetic dipole over the earth ′ s surface are expressed as the sum of three parts : a direct field of the dipole , a reflected field of image source and an absolutely convergent series of Bessel functions .

研究了一般收敛群的锥形极限集，并证明了当离散收敛群的Poincare级数收敛时，其锥形极限集的Lebesgue测度为零。

The conical limit set of convergence group is studied and that and the Lebesgue measure of the conical limit set is equal to zero when the Poincare series of discrete convergence group converge is proved .