求和公式

Gauss is a farmer's son, childhood, his math on the show extraordinary talent. Three-year-old father to correct an error in calculation; They found 10-year-old independent series of arithmetic summation of the formula; 11-year-old found the binomial theorem.

高斯是一个农民的儿子，幼年时，他在数学方面就显示出了非凡的才华。3岁能纠正父亲计算中的错误；10岁便独立发现了算术级数的求和公式；11岁发现了二项式定理。

By introducing two pairs of conjugate exponent parameters and, and using the improved Euler-Maclaurin＇s summation formula for estimating the weight coefficient, a reverse Hilbert-type inequality with a best constant factor is proved.

本文通过引入两对共轭指数参量与及应用改进的Euler-Maclaurin求和公式以估算权系数，证明了一个具有最佳常数因子的逆向Hilbert型不等式；作为应用，还给出了相应的等价式及一些特殊结果。

In this paper, we show a formula for the arciform area enclosed with a parabola and a straight line by means of two kinds of clever separation and the knowledges of elements mathematics such as the sum formula of infinite decreasing geometric sequence .

文章运用两种巧妙的分割和利用无穷递缩等比数列求和公式等初等数学知识，求出了抛物线与相交直线围成的弓形面积计算公式。

In Chapter 2, we introduce the basic knowledge of the basic hypergeometric series, including basic concepts, some summation formulas, transformation formulas, etc.

第二章：主要介绍了基本超几何级数的基本知识，包括基本概念，一些重要的求和公式以及变换公式等。

The main content of this thesis is to find and prove some summation and transformation formulae of basic hypergeometric series by the modified Cauchy method,operator method and inversion techniques,which include many well-known results as special cases,for example,q-Saalschiitz summation formula,Baileys _6ψ_6 summation formula,non-terminating Watson transformation formula and Rogers-Ramanujan identities etc.

本文的主要内容是利用修正的Cauchy方法、算子方法和组合反演技巧来发现和证明一些基本超几何级数求和公式和变换公式，其中包含一些著名的公式，如q-Saalschüz求和公式、Bailey的_6ψ_6求和公式和非终止的Watson变换公式等作为其特殊情况。

In Chapter 4, by some important summation formulas, we prove some results of number theory, such as Jacobi two square numbers theorem and Lagrange four square numbers theorem.

第四章：应用第二章介绍的几个重要求和公式，证明了数论中的若干结果。

From three respects in calculus teaching, this paper has mainly discussed magical effect of physics meaning of questions, which is curve integration curved surface integration and sum of series formula.

微积分的教学离不开问题的物理意义，文章从曲线积分、曲面积分以及级数求和公式的推导等三个方面来说明问题的物理意义在微积分教学中的妙用。

One of them contains a special case of q-Dougall summation formula,the other includes the famous Rogers-Ramanujan identities as special cases.

我们发现了两类新的基本超几何级数求和变换公式，其中一类的特殊情况包含在q-Dougall的求和公式中，另一类的特殊情况是著名的Rogers-Ramanujan恒等式。

A fast calculation approach for large-scale matrix operation, which can be accomplished by Graphic Processing Unit, was designed. For taking full advantage of the parallel architecture of GPU to enhance the calculation speed, special matrix partitioning and memory allocation mechanism according to the features of GPU were designed to decrease the frequency of data access. Meanwhile Kahan's summation formula was introduced to ensure the precision of the calculation.

设计了一种在图形处理器上完成大型矩阵快速运算的方法，主要通过使用Kahan求和公式来确保计算精度，根据GPU特点设计矩阵分块方式和内存分配机制来减少对数据访问频次，以发挥GPU的并行体系结构特性来提高计算速度。

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。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了