级数

基本解释 (translations)

progression  ·  series  ·  progressions

词组短语

theta series · number of steps

与级数相关的网络例句 [注：此内容来源于网络，仅供参考]

For some special cases, the paper gives some important identical theorems, and then establishes a valuable relation between the uniformly almost periodic functions and the trigonometric polynomials.Secondly, on the basis of the identical theorem, the paper investigates the Fourier series of the uniformly B2 almost periodic functions, and further proves that the series is unique.Thirdly, the paper discusses the Parseval equation of the uniformly B2 almost periodic functions, which establishes the relation between these functions and the coefficients of their Fourier series; and next investigates an important approximation theorem-Riesc-Fischer theorem, about the uniformly B2 almost periodic functions and the trigonometric polynomials.

并给出了特殊情况下的几个重要的恒同定理，将一致概周期函数与有限三角多项式联系起来；第二，在恒同定理的基础上，给出了一致B~2概周期函数的Fourier级数，并且级数是唯一的；第三，讨论了一致B~2概周期函数的Parseval方程，建立了函数与其Fourier级数的系数之间的联系；接着给出了关于一致B~2概周期函数和三角多项式之间的一个重要近似定理—Riesc-Fischer定理。

A series is said to be converges absolutely if the series converges; the series is called conditionally convergent, if the series converges but diverges.

绝对收敛如果级数收敛；称级数绝对收敛，如果级数收敛，而发散，则称级数条件收敛。

Theorem 1 If the power series is convergent at ,then for any that ,the power series absolutely converges at point ;if the power series is divergent at ,then for any that ,the power series diverges at point .

定理1 如果级数当时收敛，则适当不等式的一切使这幂级数绝对收敛；反之，如果级数当时发散，则适合不等式的一切使这幂级数发散。

Invariant theorem of the operator series multiplier convergent. Using operator series multiplier convergent,AK-space of concept ,we obtained the theorem of operator series multiplier convergent invariant and the old theorem of general series multiplier convergent invariant is looked as special case.

第三章 算子级数乘数收敛的不变性：利用算子级数乘数收敛、AK—空间的定义，得到了算子级数乘数收敛的不变性定理，从而将以往的普通级数乘数收敛的不变性定理作为特殊情况。

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。

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。

This paper is generaly devided into three parts,The first prepare knowledge,introduceing some conceptions asssociated with the polynomial ring and ring of power series such as power-zero element,inverse element and primitive polynomia and so on,prepare to introduce characters of power series.

本文主要分为以下三部分：首先介绍与环、多项式环、幂级数环密切相关的一些概念，如幂零元、可逆元、本原多项式等，为接下来介绍幂级数环的定义及其性质做下铺垫；然后着重讨论了环的性质，加深对多项式环与幂级数环的理解；最后讨论了多项式的性质，并将这些性质推广到幂级数环中，这也是本文的重点所在。

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。

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。

与级数相关的网络解释 [注：此内容来源于网络，仅供参考]

decreasing series：递减级数;下降级数

decreasing sequence 递减序列;下降序列 | decreasing series 递减级数;下降级数 | decrement 减量

decreasing series：递减级数;下降级数Btu中国学习动力网

decreasing sequence 递减序列;下降序列Btu中国学习动力网 | decreasing series 递减级数;下降级数Btu中国学习动力网 | decrement 减量Btu中国学习动力网

discrete power series distribution：离散幂级数分布;离散幂级数分配

离散最适设计 discrete optimal design | 离散幂级数分布;离散幂级数分配 discrete power series distribution | 离散型机率分布;离散型机率分配 discrete probability distribution

inverse factorial series distribution：逆阶乘级数分布;逆阶乘级数分配

逆元素布;反元素 inverse element | 反指数平均数 inverse exponential average | 逆阶乘级数分布;逆阶乘级数分配 inverse factorial series distribution

formal power series field：形式幂级数域

formal power series 形式幂级数 | formal power series field 形式幂级数域 | formal power series ring 形式幂级数环

Fourier series expansion syntheisis of array：陈列合成之傅式级数展开法

傅立叶级数 Fourier series | 陈列合成之傅式级数展开法 Fourier series expansion syntheisis of array | 傅式级数(天线数组)合成法 Fourier series synthesis

infinite series：无限级数;无穷级数

infinite sequence 无限序列;无穷序列 | infinite series 无限级数;无穷级数 | infinitely many 无穷多

infinite series：无穷级数,无限级数

infinite sequence 无穷序列,无限序列,无穷数列,无限数列 | infinite series 无穷级数,无限级数 | infinite set 无穷集,无限集

Laurent series：劳伦级数

级数可为整数、分 ...几何级数(Geometric Series)是劳伦级数(Laurent Series)之重要基础,读者务 ... 作者认为劳伦级数是复变分析中之最重要的观念,而几何级数又是劳伦级数之核 ...

Logarithmic series distribution：对数级数分布;对数级数分配

对数尺度 logarithmic scale | 对数级数分布;对数级数分配 logarithmic series distribution | 对数变换 logarithmic transformation