Asymptotics of any order for the eigenvalues and eigenfunctions of the Sturm-Liouville boundary-value problem on a segment with a summable potential

Abstract

For the Sturm-Liouville boundary-value problem on a segment we construct asymptotics for , where are the eigenvalues, and for the normalized eigenfunctions of the form for any , where and are expressed explicitly in terms of the potential . Under the assumption that is a real summable function, the terms and are as .