1991 Mathematics subject classification: 34B24.

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Recent results of Hald and McLaughlin concerning the inverse problem for the regular Sturm-Liouville problem on a finite interval are extended to the case in which the boundary conditions are eigenparameter dependent. Specifically, we show that the potential and the 'asymptotic' boundary conditions in such a problem are uniquely determined by a dense set of nodal points of eigenfunctions. We also simplify the proofs given by Hald and McLaughlin.

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