Col, Aynur2025-03-232025-03-2320242149-1402https://doi.org/10.53570/jnt.1501326https://search.trdizin.gov.tr/tr/yayin/detay/1270633https://hdl.handle.net/11486/3188We consider the Sturm-Liouville problem on the half line (0 ≤ x < ∞), where the boundary conditions contain polynomials of the spectral parameter. We define the scat- tering function and present the spectrum of the boundary value problem. The continuity of the scattering function is discussed. In a special case, the Levinson-type formula is intro- duced, demonstrating that the increment of the scattering function’s logarithm is related to the number of eigenvalues.eninfo:eu-repo/semantics/openAccessScattering functionLevinson-type formulaspectral parameter dependent boundary conditionArticle4811010.53570/jnt.15013261270633