When a second-order linear homogeneous differential equation is written in the form (2.3), any point at which P(x) or Q(x) becomes infinite is called a singular point or singularity. In solving a differential equation by the power-series method, one can often find the proper substitution to give a two-term recursion relation by examining the differential equation near its singularities. For the harmonic-oscillator Schrödinger equation (4.32), the singularities are at x = ∞. To check whether x = ∞ is a singular point, one substitutes z = 1/x and examines the coefficients at z = 0. Verify that exp( - ax2/2) is an approximate solution of (4.32) for very large |x|.