查询词典 summation formula

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。

Tz summation formula and an extension formula of Sears\' terminating balanced _4Φ_3 series transformation formula and an extension involving multiple sum about finite Heine\'s _2Φ_1 transformation formula are given.

应用推广后的算子，我们给出了q-Paff-Salschütz和公式的推广、Sears终止型的4Φ3变换公式的推广以及多重的有限(来源：a5ABd7C论文网www.abclunwen.com)Heine 2Φ1变换公式。

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。

Basic properties of Fouries series and the Fourier transform; Poission summation formula; convolution; mollification.

傅立叶级数和傅立叶变换的基本性质；泊松叠加方程；卷积；缓和？

A convergence acceleration technique based on functional asymptotic expansion and Poisson's summation formula is developed to raise the calculation efficiency of waveguide dyadic Green's functions which are expanded in infinite series.

为此，作者提出"谱展开边界元法"，以求解波导外空间的并矢Green函数；引入边界元法以求解波导壁内折曲缝隙腔的并矢Green函数；并研究了无穷级数的逐级加速收敛变换，以解决波导中Green函数的计算问题。

Finally, another generalization of Gasper's bibasic summation formula is also obtained.

并给出了Gasper双基和公式的另一个推广形式。

As applications of Gasper's matrix inverse, we generalize Jackson's bibasic summation formula 40,

并且具体的讨论了带参数（a，q，2）的Bailey对和带参数（a，q，3）的Bailey对的具体应用。

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。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。