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在文章的第二部分，我们考虑了双超几何项的递推公式。In part II, we consider the recurrence formula of double hypergeometric terms.

本文用超几何函数来表示倾角函数。In this paper, the inclination functions are expressed as the hypergeometric functions.

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解的零级近似可以用汇合超几何函数表示。The zeroth order approximation of the solution can be expressed in terms of confluent hypergeometric functions.

在文章的第二部分，我们考虑了双超几何项的递推公式。Furthermore, some new Rogers-ramanujan type identities are obtained by a transformation of basic hypergeometric series.

为了提高计算效率，作者将这些系数用超几何函数予以表示，并由此提出了高效的计算方法。These coefficients are expressed by the hypergeometric functions and a method with high efficiency in computations in presented.

计算矩阵变量超几何函数的关键在于带状多项式的计算。Efficient calculating method for zonal polynomials is the key of good approximation for hypergeometric function with matrix argument.

本文运用基本超几何级数求和的一个简单算法，求得一些基本超几何级数的求和公式。By using a simple algorithm for the summation of basic hypergeometric series, summation formulas for some basic hypergeometric series are obtained.

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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.

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

本文研究了一类离散型随机变量的概率分布，称之为负几何分布和负超几何分布。A class of discrete type random variable probability distributions, called negative geometric distribution and negative hypergeometric distribution, are discussed.

并利用束缚态边界条件，获得了束缚态能谱表达式和由超几何函数表示出的波函数。With the boundary conditions of bound states, we have obtained the corresponding energy spectrum via an expression and wave functions in terms of hypergeometric functions.

径向束缚态波函数用合流超几何函数表示，束缚态的能量方程可由径向波函数满足的边界条件得到。The radial bound state solutions are expressed in terms of the confluent hypergeometric functions and the energy equation is derived from the boundary condition satisfied by the radial wavefunctions.