Sturm–Liouville problems with boundary conditions rationally dependent on the eigenparameter, II

Necessary and sufficient conditions are given for two sequences λn and ρn to be the eigenvalues and norming constants of a Sturm–Liouville boundary value problem −y″+qy=λy, y(0) cos α=y′(0) sin α and y′(1)=f(λ)y(1) where f is a rational function of Herglotz–Nevanlinna type. It is also proved that q, α and f are uniquely determined by the sequences λn and ρn.