超几何级数

In the last chapter we derive new identities frominversion and famous hypergeometric series identities.

在最后一章里，我们利用-反演和一些著名的超几何级数恒等式，得到了一些形式比较漂亮的新的恒等式。

In chapter 4,by the inversion technique and the series rearrangement,we find two kinds of transformation formulae of the basic hypergeometric series.

第四章结合反演技巧和级数重排的方法研究基本超几何级数。

During this period, his research magic square, chain fraction, hypergeometric series , elliptic integrals and some ...

在这段期间，他自己研究魔方阵、连环分数、超几何级数、椭圆积分及一些。。。

During this period, he studies magic square, chain fraction, hypergeometric series , elliptic integrals and some ...

在这段期间，他自己研究魔方阵、连环分数、超几何级数、椭圆积分及一些。。。

In this thesis, we mainly discuss the applications of matrix representation of inverse relations to the WZ theory and to the hypergeometric series identities.

本文主要讨论反演关系的矩阵表示在WZ理论中的一些应用及由-反演和著名的超几何级数恒等式推出形式比较漂亮的新的恒等式。

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。

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。

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。

5 Involving four arbitrary sequences and other general bilateral summations.

并由此得到了几个基本超几何级数求和公式及其极限情况。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。