  In 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 $A_n(\lambda)$ 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 $\Gamma_q$-function.
