  We extend the recently developed Izergin-Korepin analysis on the
wavefunctions of the $U_q(sl_2)$ six-vertex model to the reflecting boundary
conditions. Based on the Izergin-Korepin analysis, we determine the exact forms
of the symmetric functions which represent the wavefunctions and its dual.
Comparison of the symmetric functions with the coordinate Bethe ansatz
wavefunctions for the open XXZ chain by Alcaraz-Barber-Batchelor-Baxter-Quispel
is also made. As an application, we derive algebraic identities for the
symmetric functions by combining the results with the determinant formula of
the domain wall boundary partition function of the six-vertex model with
reflecting end.
