A novel generalized solution expansion for the Lagerstrom model

In this paper we re-visit the Lagerstrom problem y + n − 1 r y + eyy = 0, y(1) = 0, y(∞) = 1, where e is a small positive real number and n is a positive integer (or any real number greater than 2). Using rigorous analysis, a generalized asymptotic expansion, as e → 0, is derived for the solution of this problem. A trans-series expansion of the solution for large values of r is also presented; the leading term coefficient is determined by a connection formula between the values of the solution at the two points r = 1a ndr = ∞. An extension and a discussion of the problem for n ∈ (1, 2) is also given.