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