An equation of Ince: The confluent Mathieu equation (Q1200041)

The author studies the second order linear differential equation of the form \(xY''+{1\over 2}Y'+(A-B^ 2x-Kx^ 2)Y=0\) which has two singularities: an elementary singularity at the origin and an irregular singularity of the third type at infinity. He exhibits an explicit solution of this equation in the form of power series and investigates asymptotic properties of solutions at infinity.