![]() For the problem on the half-line, a new efficient formula is given for the first term of the well-known Coulson–March expansion of the solution in a neighborhood of infinity, and generalizations of this representation and its analogues for the inverse of the solution are obtained. Assuming that the exponent in the coefficient of the nonlinear term is rational, new parametric representations are obtained for the solution of the boundary value problem on the half-line and on the interval. A two-point boundary value problem is considered for the Emden–Fowler equation, which is a singular nonlinear ordinary differential equation of the second order.
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