Approximate Calculation of Eigenvalues and Eigenfunctions of One Discontinuous Boundary Value Problem Kadriye AYDEMİR , Oktay MUHTAROĞLU and Adem EROĞLU [email protected], [email protected], [email protected] Gaziosmanpaşa University, Tokat, In this paper is considered a new boundary value problem consisting of eigen parameter-dependent boundary and transmission conditions at interior points, as well as at the end points of the interval. Our goal is to establish asymptotic formulae (with an arbitrary number of terms) for the eigenvalues and eigenfunctions. In particular we find asymptotic formulas for the eigenvalues and eigenfunctions. Keywords. Boundary value problem, eigenvalue, eigenfunction, asymptotics of eigenvalues and eigenfunction. AMS 2010. 34B24, 34L15 References  K. Aydemir and O. Sh. Mukhtarov Green's Function Method for Self-Adjoint Realization of Boundary-Value Problems with Interior Singularities, Abstract and Applied Analysis, vol. 2013, Article ID 503267, 7pages, 2013. doi:10.1155/2013/503267.  Mukhtarov, O. Sh. and Yakubov S., Problems for Ordinary Differential Equations with Transmission Conditions, Applicaple Analysis, 81, 1033-1064, 2002.  Titchmars, E. C., Eigenfunctions Expansion Associated with Second Order Differential Equations I, second edn. Oxford Univ. press, London , 1962.  Zettl, A., Adjoint and Self-adjoint Boundary Value Problems with Interface Conditions, SIAM J. Appl. Math. 16, 851-859, 1968.  Woldegerima , W. A., The Sturm-Liouville Boundary Value Problems and their applications: First Edition, LAP Lambert Academic Publishing, 2011 .