2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62907We apply a method of perturbation for the $BC_1$ Inozemtsev model from the trigonometric model and show the holomorphy of perturbation.Consequently, the convergence of eigenvalues and eigenfuncions which are expressed as formal power series is proved. We investigate also the relationship between $L^2$ space and some finite dimensional space of elliptic functions.30 pages, to appear in Electronic Journal of Differential EquationsClassical Analysis and ODEsMathematical PhysicsSpectral TheoryExactly Solvable and Integrable Systems33E15; 81Q10text