Asymptotic expansion of differential equations with an irregular singular point of finite rank

An asymptotic expansion is constructed for solutions of second-order differential equations with an irregular singular point of finite rank at infinity. Formal solutions are obtained. By reduction of the differential equation to a Volterra integral equation we prove that the formal solutions are asymptotic expansions of the solutions of the differential equation.Simferopol' University. Translated from Dinamicheskie Sistemy, No. 10, pp. 78–83, 1992.