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Symbolic analytical solution of N-dimensional radially symmetric polytropes

A. S. Saad
Organization: National Research Institute of Astronomy and Geophysics, Cairo, Egypt
Department: Department of Astronomy
Journal / Anthology

Astronomische Nachrichten
Year: 2004
Volume: 325
Issue: 9
Page range: 733-739

In this paper, accelerated power series solutions are developed for N-dimensional symmetric radially polytropes. The solutions are valid for any geometric and polytropic index. The implementation of PadŽe technique and changing of the independent variable give us identical polytrope solutions to the numerical one. Physical parameters are presented for Ndimensional radially polytropes. In case of the isothermal sphere, the density profile is accurate to 10−5 per cent whatever the value of ξ is. All the computations are performed using Mathematica software.

*Mathematics > Calculus and Analysis > Differential Equations
*Mathematics > Calculus and Analysis > Series
*Mathematics > Geometry > n-Dimensional Geometry
*Science > Astronomy
*Science > Physics > Astrophysics
*Wolfram Technology > Programming > Equation Solving

stars, sun, power series, Pade approximants, Lane-Emden equations