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Developments in determining the gravitational potential using toroidal functions
Author(s) -
Cohl H.S.,
Tohline J.E.,
Rau A.R.P.,
Srivastava H.M.
Publication year - 2000
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/1521-3994(200012)321:5/6<363::aid-asna363>3.0.co;2-x
Subject(s) - physics , toroid , azimuth , cylindrical coordinate system , coordinate system , mathematical analysis , spherical coordinate system , invariant (physics) , fourier series , laplace's equation , fourier transform , gravitation , laplace transform , gravitational potential , series expansion , classical mechanics , mathematical physics , geometry , mathematics , boundary value problem , mechanics , optics , quantum mechanics , plasma
Cohl & Tohline (1999) have shown how the integration/summation expression for the Green's function in cylindrical coordinates can be written as an azimuthal Fourier series expansion, with toroidal functions as expansion coefficients. In this paper, we show how this compact representation can be extended to other rotationally invariant coordinate systems which are known to admit separable solutions for Laplace's equation.