超几何级数

Basic hypergeometric series(also called q-series)plays an important and special role in combinatorial analysis,special functions and number theory,and is widely applied in statistics and physics etc.

基本超几何级数，又称q-级数，在组合分析、特殊函数以及数论等领域起着重要而又特殊的作用，并且广泛地应用于统计学理论和物理等方面。

He hypergeometric series, a complex function, statistical mathematics, elliptic function of both major contribution.

他对超几何级数、复变函数、统计数学、椭圆函数论都有重大贡献。

This dissertation studies the applications of the inversion techniques and its equivalent form in finding and proving the hypergeo...

本文探讨了反演技术及其等价的形式在寻求和证明超几何级数恒等式方面的应用。

This dissertation studies the applications of the inversion techniques and its equivalent form in finding and proving the hypergeometric series identities.

本文探讨了反演技术及其等价的形式在寻求和证明超几何级数恒等式方面的应用。

Such as,the generating function and the q-Mehler formula of this polynomials.

作为应用，我们还给出了基本超几何级数的一些形式扩张公式。

The main contents of this thesis can be summarized as follows:In Chapter 1, we introduce the development of the basic hypergeometric series.

论文的主要内容如下：第一章：简要地介绍了基本超几何级数的发展概况。

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。

In the thesis, the basic knowledge of the basic hypergeometric series, some results of the Rogers-Ramanujan type identities and its applications in number theory are studied.

本文主要介绍了基本超几何级数的基本内容，关于Rogers-Ramanujan类型恒等式的一些结果以及基本超几何级数在数论中的若干应用。

In Chapter 1,we first look back the history of hypergeometric series and basic hy-pergeometric series,and then introduce some necessary concepts and notations.

第一章首先回顾超几何级数与基本超几何发展的历史，然后引进一些必要的概念和记号。

By using this method we obtain two gen-eralized transformation formulae of q-integral form,two identities of basic hypergeometric series,as well as formal extensions for q-Pfaff-Saalschütz formula,q-Chu-Vandermonde identity and a three-term transformation formula of _3φ_2-series.

我们推广了两个q-积分形式的变换公式和两个有关基本超几何级数的恒等式，还得到q-Pfaff-Saalschütz公式、q-Chu-Vandermonde恒等式和基本超几何级数中一个有关_3φ_(2~-)级数的三项变换公式等的形式推广。

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。