2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159565In this contribution we give an explicit formula for the eigenvectors of Hamiltonians of open Bazhanov-Stroganov quantum chain. The Hamiltonians of this quantum chain is defined by the generation polynomial $A_n(λ)$ which is upper-left matrix element of monodromy matrix built from the cyclic $L$-operators. The formulas for the eigenvectors are derived using iterative procedure by Kharchev and Lebedev and given in terms of $w_p(s)$-function which is a root of unity analogue of $Γ_q$-function.Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/Exactly Solvable and Integrable SystemsStatistical MechanicsMathematical Physicstext