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Asymptotic solutions for the Sturm-Liouville boundary value problem with interior singularities were obtained using asymptotic forms of the Whittaker functions for higher order modes and the Titchmarsh-Weyl m-function for low order modes. However, these split interval techniques do not readily provide the eigenrelations for low order modes. For the first time, with minimal constraints, the eigenvalues for the Sturm-Liouville eigenproblem are obtained when the Titchmarsh-Weyl m-function technique is employed.

Derivation of eigenrelations for the Sturm-Liouville boundary value problems with interior singularities