New methods for analytical calculation of elliptic integrals, applied in various physical problems
Abstract
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.
Cite
@article{arxiv.2301.00643,
title = {New methods for analytical calculation of elliptic integrals, applied in various physical problems},
author = {Bogdan G. Dimitrov},
journal= {arXiv preprint arXiv:2301.00643},
year = {2023}
}
Comments
19 pages, Revtex 4.0; no figures, Talk at the Fourteenth Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 22-27, 2022; prepared for the Proced. of the AIP