Power-series solutions of the Lane-Emden equation

Details Power-series solutions of the Lane-Emden equation Power-series solutions of the Lane-Emden equation

Nov 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980ap%26ss..73..227m&link_type=abstract

Astrophysics and Space Science, vol. 73, no. 1, Nov. 1980, p. 227-239.

Astronomy and Astrophysics

Astrophysics

7

Astrophysics, Nonlinear Equations, Polytropic Processes, Power Series, Stellar Structure, Convergence, Differential Equations, Numerical Integration, Singularity (Mathematics)

Scientific paper

The Lane-Emden equation is a nonlinear second-order differential equation that governs the structure of a polytropic gas sphere in equilibrium under its own gravitation; for values of the polytropic index between 0 and 5, the equation approximates to a reasonable accuracy the structures of a variety of realistic stellar models. This paper considers the problem of representing the numerical solutions of the Lane-Emden equation analytically by means of a convergent power series. It is shown that it is possible to represent these solutions by a power series which can be convergent in the whole interior of a polytropic model.

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