超几何函数

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。

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 .

超几何函数在量子力学上的应用

Applications of ( confluent ) hypergeometric functions in quantum mechanics

OS代数的机器计算与介孔分子势能的超几何函数表示

Computation of Orlik-Solomon Algebra and Hypergeometric Function Expressions for the Molecule-Micropore Potential

经构造两个邻次超几何函数的恒等式，可以证明用模数k与k1表示的第一、二两种全椭圆积分的一个替换公式。

Constructing an identity of two adjacent hypergeometry function , a replacement formula which was expressed by modulus k_1 and k_2 can be proved .

Pade′逼近（∈&算法）和超几何函数的快速收敛

Application of the Pade ' Approximant (∈ & Algorithm ) to the Convergence Acceleration of the Hypergeometrical Function

文中通过引入一个位移函数H（ξ），将该问题的方程组化成一个关于H（ξ）的6阶常微分方程，用广义超几何函数给出问题的精确解。

In this paper , the governing equations of the problem have been changed into a six-order ordinary differential equation about the displacement function H (ξ) , the exact solution of the six-order equation was given in generalized hypergeometric function .

云中凝结核CCN的数浓度采用超几何函数表示；

The number concentration of the activated cloud condensation nuclei ( CCN ) is described with the hypergeometric function .

文中采用矩母函数分析方法，通过引入超几何函数，详尽推导出Rayleigh衰落信道下的多点合作通信系统的平均符号错误率和中断率的精确闭式表达式。

Exact and closed-form expressions of average symbol error rate ( SER ) and outage probability with Rayleigh fading channels was firstly derived by means of the moment generating function ( MGF ) with hyper-geometric function .

给出了具有Manning-Rosen型标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态解，其解可用超几何函数表示。

The s-wave bound states of the Klein-Gordon equation and Dirac equation with equal Manning-Rosen scalar and vector potentials are obtained , and the solutions are expressed by the hypergeometric function .

四次非谐振子能级的超几何函数解

Hypergeometric Function Solutions of the Energy Levels for Quartic Anharmonic Oscillator

用超几何函数证明全椭圆积分的一个替换公式

The proof of a total elliptical integral replacement formula with the hypergeometric function

一类超几何函数比的几个不等式

Some inequalities for the ratios of hypergeometric functions

星象的广义超几何函数

Starlike Generalized Hypergeometric Functions SUPERPOTENTIAL AND GENERALISED POTENTIAL

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 func-tions .

用合流超几何函数统一了量子力学若干问题的解法；

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

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 .

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 .

对于两种类型的边界条件，应用超几何函数和反演技术得到了问题的解析解，并分析了指数弥散过程和常数弥散过程的不同性质。

According to the analytical solution and computing results the difference between the exponential dispersion and constant dispersion process is analyzed .

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。

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

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。

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

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 .

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；

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 ;

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。

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 .