In this paper, we apply the collocation method for solving some classes of Lane-Emden type equations that are determined in interval $[0, 1]$ and semi-infinite domain. We use an orthogonal system of functions, namely Gegenbauer polynomials and introduce the shifted Gegenbauer polynomials and the rational Gegenbauer functions as basis functions in the collocation method for problems in interval $[0, 1]$ and semi-infinite domain, respectively.
We estimate that the proposed method has super-linear convergence rate
and also investigate the Gegenbauer parameter $ (\alpha)$ to get more accurate answers for various Lane-Emden type problems. The comparison between the proposed method and other numerical results shows that the method is efficient and applicable.