Numerical determination of the Titchmarsh-Weyl m-coefficient and its applications to HELP inequalities

Abstract

This paper is concerned with numerical methods for finding m(λ), the Titchmarsh-Weyl m-coefficient, for the singular eigenvalue equation -y" + qy = λy on [0, ∞) and the results are applied to the problem of finding best constants for Everitt’s extension to the Hardy-Little-wood-Pόlya (HELP) integral inequality.