hypergeometric functions

Applications of ( confluent ) hypergeometric functions in quantum mechanics

超几何函数在量子力学上的应用

These coefficients are expressed by the hypergeometric functions and a method with high efficiency in computations in presented .

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。

The solutions of some quantum mechanics questions are unified by confluent hypergeometric functions ;

用合流超几何函数统一了量子力学若干问题的解法；

Properties of Analytic Functions Defined by Hypergeometric Functions ; By using the curve-fitting method , its analytical expression is obtained .

用超几何函数定义的解析函数的性质并以曲线拟合法求得该函数的解析表达式。

Some inequalities for the ratios of hypergeometric functions

一类超几何函数比的几个不等式

The zeroth order approximation of the solution can be expressed in terms of confluent hypergeometric functions .

解的零级近似可以用汇合超几何函数表示。

Explain confluent hypergeometric functions and hypergeometric functions are better model functions by the relations between the two kinds of functions in common use functions .

通过超几何函数、合流超几何函数与常用函数的关系说明它们是很好的原型函数。

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 .

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。

Starlike Generalized Hypergeometric Functions SUPERPOTENTIAL AND GENERALISED POTENTIAL

星象的广义超几何函数

With the help of a transformation formula of basic hypergeometric functions , known identities , and Jacobi triple , we have established some new Rogers-Ramanujan type identities .

本章借助一个基本超几何函数的变换公式、已知的恒等式以及Jacobi三重积，建立了一些新的Rogers-Ramanujan型恒等式。

The second part is about hypergeometric functions which are studied in chapters 5 and 6 . These two parts are not interrelated clearly in real space , but they have essential relations in complex space .

这两部分在实空间中是不大相关的，但在复空间中有密切的联系。

By using the expansion of spherical wave functions for a cylindrical wave function and the techniques of the hypergeometric functions , the Sommerfeld integral contained in the potential is expressed as a rapidly and absolutely convergent series of spherical wave functions ;

利用圆柱波函数的球面波函数展开式和超几何函数理论，位函数中的索末菲尔德积分被表示成快速、绝对收敛的球面波展开式；

For calculating integrals involving four confluent hypergeometric functions , a general theoretical method is presented , which is valid for both symmetric and asymmetric geometries to determine the triple differential cross sections ( TDCS ) for electron impact ionization of ions .

解决了包含四个合流超几何函数的数值积分问题，从而给出了计算电子碰撞电离离子三重微分截面的通用方法，适合于中、高入射能量下的各种几何条件。