椭圆积分解析计算的新方法，应用于各种物理问题
New methods for analytical calculation of elliptic integrals, applied in various physical problems
摘要：
本文简要介绍了椭圆积分在GPS（全球定位系统）通信（解释了广义相对论效应）、宇宙学、黑洞物理学和天体力学中的广泛应用。结合椭圆函数理论中的几种方法，提出了一种新的零阶Legendre型椭圆积分的解析计算方法：1.高阶椭圆积分的两种不同表示的递归方程组。2.用维尔斯特拉斯椭圆函数对四维代数方程进行单值化3.变量变换，与新变量成反比（二次）。所开发的方法是一个向前迈出的一步，构建分析方法，可以提高精度的计算椭圆积分，必要的理论和实验问题。
英文摘要：
A short review will be made of elliptic integrals, widely applied in GPS (Global Positioning System) communications (accounting for General Relativity Theory-effects), cosmology, Black hole physics and celestial mechanics. Then a novel analytical method for calculation of zero-order elliptic integrals in the Legendre form will be presented, based on the combination of several methods from the theory of elliptic functions: 1. the recurrent system of equations for higher-order elliptic integrals in two different representations. 2. uniformization of four-dimensional algebraic equations by means of the Weierstrass elliptic function 3.a variable transformation, inversely (quadratically) proportional to a new variable. The developed method is a step forward towards constructing analytical methods, which can improve the precision of the calculation of elliptic integrals, necessary both for theoretical and experimental problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
