级数的

The techniques of computing the domain of convergence and sum function and expanding functions in several variables to power series of functions in several variables are mainly discussed by many examples.

引入了多元函数项级数的概念，给出了其收敛域及和函数的定义；通过详实的例子讨论了多元幂级数的收敛域、和函数及多元函数展开为多元幂级数的计算方法。

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。

Chapter 1 outlines the research development of Dirichlet series, and presents the main results obtained in the thesis.

第二章研究了三重Dirichlet级数和n重Dirichlet级数的收敛性，同时在一定的条件下研究了三重随机Dirichlet级数的收敛性。

Definition The infinite series converges and has sum if the sequence of partial sums converges to ,that is .If diverges, then the series diverges. A divergent series has no sum.

定义如果级数的部分和数列有极限，即，则称无穷级数收敛，这时极限叫做这级数的和，并写成；如果没有极限，则称无穷级数发散。

They are the deflection w, the rotations of the normal to the undeformed median surface Φx,Φy and the force function F. In the present paper these dependent functions are expressed as generalized double Fourier series with beam eigenfunctions as general terms.

本文中将这四个独立的函数表示为广义傅里叶级数，选用了两个变量分离的梁本征函数之积构成广义傅里叶级数的通项，通过梁本征函数中的待定常数使所选级数预先满足简支、固支或弹性支持边界条件。

Integral of one variable functions, improper integral and its convergence properties.

本课程的主要内容包括：1 各种极限运算，其中包括数列极限、函数极限以及上、下极限；2 一元函数的微分学，包括微分和导数的运算法则、微分中值定理及其应用等；3 一元函数的积分和广义积分及其收敛性；4 级数及其收敛性，包括数值级数的收敛性和函数项级数的各种运算和性质；5 多元函数的微分学及其应用，其中很多方面与一元函数的微分学近似，需要注意它们之间的区别；6 多元函数的积分学，包括多重积分的性质与计算，多重积分的的应用等；7 曲线、曲面积分及其应用；8 含参变量积分的计算与性质；9 Fourier 级数及其应用，等等。

It is complete for continuous functions on [0,1] (C[0,1]), and the properties of quick transformation and other well properties similar to Fourier system, but its partial sum is superiority to Fourier system as the approaching tool.

在此函数系上展成的Fourier级数有许多与三角Fourier级数相似的性质，三角形Fourier级数的部分和在作为函数的逼近工具时确实要比三角Fourier级数优越一些。

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。

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。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。