Inversion problems in the \(q\)-Hahn tableau (Q1971736)

If \(\{P_n(x;q)\}\) is a family of polynomials belonging to the \(q-\)Hahn tableau (see \textit{T. H. Koornwinder} [Pitman Res. Notes Math. Ser. 311, 46-128 (1994; Zbl 0821.17015)]) then each polynomial of this family can be written as \(P_n(x;q)=\sum_{m=0}^n D_m(n)\vartheta_m(x)\) where \(\vartheta_m(x)\) stands for \((x;q)_m\) or \(x^m\). In this paper the corresponding inversion problem is solved, that is, the explicit expression is found for the coefficients \(I_m(n)\) in the expansion \(\vartheta_m(x)=\sum_{m=0}^n I_m(n) P_m(x;q)\). The algorithm, called Navima, can be obtained from \url{http://www.uvigo.es/webs/t10/navima}.