Exact solutions of the generalized Lane-Emden equation

A generalized Lane-Emden equation with indices (alpha,beta,nu,n) is discussed, which reduces to the Lane-Emden equation proper for alpha=2, beta=1, nu=1. General properties of the set of solutions of this equation are derived, and exact solutions are given. These include a singular solution without free integration constant for arbitrary n and for particular relations between n, nu, and alpha. Among the two-parameter solutions nonequivalent families of solutions of the same equation are obtained. (C) 2000 American Institute of Physics. [S0022-2488(00)03510-6].