Singularities of sturm-liouville expansions for second order ordinary differential equations : II

Abstract

The authors investigate the correspondence between the singularities of Sturm-Liouville expansions of the form ?_n v_n(z), Where the v_n(z) are the normalized eigenfunction expansions of a regular second order Sturm-Liouville eigenvalue problem, with the singularities of the power series a_n ^{a n}. It is shown if is a singularity of power series on its radius of convergence then the Sturm-Liouville series is singular at both the points z₁=arg?-iin|?|,and z₂=-z₁