ORIGINAL_ARTICLE Inverse Nodal Problem for Polynomial Pencil of a Sturm-Liouville Operator from Nodal Parameters A Sturm-Liouville problem with n-potential functions in the second order differential equation and which contains spectral parameter depending on linearly in one boundary condition is considered. The asymptotic formulas for the eigenvalues, nodal parameters (nodal points and nodal lengths) of this problem are calculated by the Prüfer's substitutions. Also, using these asymptotic formulas, an explicit formula for the potential functions are given. Finally, a numerical example is given. https://mir.kashanu.ac.ir/article_111634_89d6dc1051dd147639c7ebc8f42970d0.pdf 2021-09-01 171 183 10.22052/mir.2021.242239.1286 Eigenvalues Eigenfunctions Prüfer's Substitutions Sturm-Liouville problem Inverse Nodal problem Sertac Goktas srtcgoktas@gmail.com 1 Department of Mathematics, Mersin University, Mersin, Turkey LEAD_AUTHOR Esengul Biten esengulbiten@gmail.com 2 Department of Mathematics, Mersin University, Mersin, Turkey AUTHOR  V. Ala and Kh. R. Mamedov, On a discontinuous Sturm-Liouville problem with eigenvalue parameter in the boundary conditions, Dynamic Syst. Appl. 29 (2020) 182 − 191. 1  V. A. Ambartsumyan, Über eine Frage der Eigenwerttheorie, Zeitschrift für Physik 53 (1929) 690 − 695. 2  G. Birkhoff and G. C. Rota, Ordinary Differential Equations, 4th ed., Ginn, John Wiley & Sons, Boston, 1989. 3  G. Borg, Eine umkehrung der Sturm-Liouvilleschen eigenwertaufgabe, Acta Math. 78 (1) (1946) 1 − 96. 4  P. J. Browne and B. D. 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