椭圆积分

Legendre椭圆积分在物理学中的应用

The application of Legendre elliptic integral function in physics

在计算OH线圈的电磁分布和电感时，应用毕奥-沙伐公式，通过椭圆积分简化计算，然后把求解过程转化成计算机语言，经反复调试和修改得到一个满足要求的结果。

In calculating the magnetic distribution and the inductance of OH coil , Bill-Surf equation and elliptic integral is used to simplify the calculation , Then , turn processes of calculation into language for computers , and a right result has been received after a series of adjustments .

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 .

Muir平均与第二类完全椭圆积分

The Muir Mean And The Complete Elliptic Intergral of The Second Kind

Cap-cyclide坐标中Jacobi第一种完全椭圆积分和Jacobi椭圆函数的数值计算

Numerical Calculation of the First Jacobi Entire Oval Integral of Jacobi oval function in Cap-cyclide coordinate

在简化过程中，把原来的表达式设法用Fourier级数来表示，但只取二阶谐波为限；同时，又找到两个代数式来代替两个椭圆积分。

The distribution is approximated by a Fourier series to the second harmonics , and in order to facilitate integration process , two algebraic expressions are used to replace the complete elliptic integrals of the first and second kinds .

本文对Cap-cyclide坐标下，Jacobi第一种完全椭圆积分和Jacobi椭圆函数的各种计算方法进行了数值计算，通过分析和比较进而得出了最佳方法。

In this paper , it numerically calculates every kind of calculation method of the first Jacobi entire oval integral and Jacobi oval function in Cap-cyclide coordinate . By analysising and comparing , the paper has finally reached the optimum method .

本文介绍了三种具有较高计算精度的螺线管线圈磁场的计算方法，并对它们的计算精度进行了比较。这三种方法是：勒让德函数展开法，单积分法和椭圆积分的Bartky变换法。

In this paper three precise magnetic field calculation methods and their comparison for solenoid coil are discussed , which are : Legendre Polynomial Expansion Method , A single Integral Formula Method and Bartky Transformation Method of Elliptic Integral Calculation .

研究椭圆积分物理问题的一种方法

A method for qualitative research of physical problems on elliptic integrals

第一类完全椭圆积分一种未完全发育的圆蛤。

Complete elliptic integral of the first kind a half-grown quahog .

椭圆积分方程的快速数值求解与误差分析

Fast Numerical Method and Error Analysis of Ellipse Integral Equation

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

椭圆积分在玻璃钢缠绕技术中的应用

Application of Ellipse Integral in Winding Technique for GRP

利用椭圆积分法计算某些电磁场问题

The calculations of some electrostatic and magnetostatics problems by means of elliptic integral

椭圆积分的一种新型计算法

A new method for calculating ellipse integral

完全椭圆积分的初等逼近

Elementary Approximations for Complete Elliptic Integrals

特别地，作者运用此法则，证明并改进了关于完全椭圆积分的一个猜测。

In particular , a conjecture on complete elliptic integrals is proved to be true and improved .

应用第一类完全椭圆积分求出了非线性振动周期的精确解。

The exact solution of the period is got by using the first kind of complete elliptic integral .

这样一种分类称为图的一个二分类。第二类完全椭圆积分

Such a partition is called a bipartition of the graph . complete elliptic integral of the second kind

但实际的单摆运动的分析求解将会导致没有解析解的椭圆积分。

The relative analysis and resolving usually lead to the elliptic integral which is difficult to be resolved .

采用变分迭代法对系统的跌落冲击微分方程进行求解，用椭圆积分法对其进行了验证。

The dropping impact differential equation was solved by the variation iteration method and verified by the elliptic integral method .

本文利用完全椭圆积分的某些组合之性质，给出了M.K.Vamanamurthy和M。

By means of properties of certain combinations of complete elliptic integrals , the authors provide a negative answer to M. K.

问题的讨论有助于我们掌握解决涉及椭圆积分物理学问题的方法。

Discussion on the problem may help us to master the method solving this kind of the physics problem of elliptic integrals .

采用0.618法来进行椭圆积分值的查寻，编制的计算机程序计算速度快。

The golden section ( 0.618 ) approach is also used to look forthe elliptic integrals and the program developed with the formulas is of high computingspeed .

本文用数值方法求解含有椭圆积分的二阶微分方程，讨论了均匀带电圆环内点电荷的非线性振荡及其运动特征。

The second-order differential equation including elliptic integral is numerically solved by integral , and the non-linear oscillation of a charged point in a uniformly charged ring is discussed .

揭示了一类重要的特殊函数&广义椭圆积分以及Γ-函数、Ψ-函数等相关特殊函数的一些性质。

In this paper , some properties are obtained for the generalized elliptic integrals , which are very important special functions , and for some other related special functions .

均匀带电圆环所在平面上的场与全椭圆积分的替换公式对均匀带电圆环环面上电势与场强的分析

ELECTRIC FIELD AT THE PLAIN OF THE UNIFORM CHARGED RING AND SUBSTITUTION FORMULA OF THE ELLIPTICAL INTEGRAL The Analysis of Potential and Field Strength Evenly Distributed on the Charged Ring Plane

基于大挠度理论，考虑初始偏心的影响，通过积分变换及椭圆积分展开式推导得到压力与初始偏心之间公式。

Based on the large displacement theory , and with consideration of initial eccentricity , the relation formula between pressure and initial eccentricity is deduced through integral transform and elliptic integral .

然后利用幂级数展开方法将被积函数表示为级数的形式；再经过简单的积分计算将椭圆积分表示为级数；

By using power series expansion method , the integrand is expressed as the form of a series , and then the ellipse integral is expressed as a series through simple integration .

并归结为四个积分，其中三个积分有封闭形式的精确解，第四个可化为椭圆积分，或用数值法计算。

As a result , four integrals are involved , three of which can be given in closed form and the fourth can be expressed in terms of elliptic integrals or be evaluated numerically .