Approximate analytic solutions of the Lane-Emden equation for positive integer values of polytropic index

Authors

Rogel Mari Sese ⋅ PH Institute of Mathematical Sciences and Physics, University of the Philippines Los Baños and National Institute of Physics, University of the Philippines Diliman
Jose Perico Esguerra ⋅ PH National Institute of Physics, University of the Philippines Diliman

Abstract

Analytic solutions of the Lane-Emden equation exists only for polytropic indices n = 0, 1, and 5. Here, we derived an approximate analytic solution using the power series expansion ofthe polytropic function. We performed Laplace transformation and Padé approximation in transform space followed finally by an inverse Laplace transformation to obtain the analytic expression and demonstrated that the new form is convergent for integral values of the polytropic index.

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Issue

2003: Proceedings of the 21st Samahang Pisika ng Pilipinas Physics Congress

Article ID

SPP-2003-PA-25

Section

Poster Session PA

Published

2003-10-22

How to Cite

[1]

RM Sese and JP Esguerra, Approximate analytic solutions of the Lane-Emden equation for positive integer values of polytropic index, Proceedings of the Samahang Pisika ng Pilipinas 21, SPP-2003-PA-25 (2003). URL: https://proceedings.spp-online.org/article/view/SPP-2003-PA-25.