Recursion relations for the canonical solution of Sturm-Liouville problem with turning points

Abstract

The paper studies the differential equation y’’+(ρ2φ2(x)−q(x))y=0,on a finite interval I, say I=[0,1], where I contains m turning points, x1,x2,...,xm, that is, zeros of φ. We show that if one obtains the canonical solution of an initial value problem generated by the equation in the interval [0,x1), the canonical solutions in the remaining intervals can be obtained recursively.