New methods for analytical calculation of elliptic integrals, applied in various physical problems

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 integra...

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Bibliographic Details
Published in:arXiv.org 2022-12
Main Author: Dimitrov, Bogdan G
Format: Article
Language:English
Subjects:
Celestial mechanics
Communications systems
Cosmology
Elliptic functions
Mathematical analysis
Relativity
Online Access:Get full text
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Summary: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.
ISSN:2331-8422