Eigenvalue and Eigenfunction Asymptotics for Regular Sturm-Liouville Problems

In this paper, we obtain asymptotic formulas for eigenvalues, eigenfunctions, and the reciprocals of the eigenfunction norms for eigenvalue problems associated with the general Sturm-Liouville equation (pu′)′ + (λr − q)u = 0 having regular endpoints. The method is based on a conversion to Liouville Normal Form and an iterative procedure of solving the associated Volterra integral equation, producing an asymptotic expansion of the solution in higher powers of 1/λ1/2 as λ → ∞.