Asymptotical basis of solutions of $q$-recurrence relations outside of the zone of clustering eigenvalues

A procedure for constructing expansions of the basis of solutions of a four-term recurrence relations with coefficitnts from the ring $\mathbb{Z}[q,1/q]$ is described. The fact that outside of the zone of the clustering eigenvalues these expansions are the asymptotical expansions is proven.