Methods for computing $q$-polynomials

The methods of computing the classical orthogonal polynomials of a discrete variable (called qpolynomials) are considered. Some difficulties connected with the instability of a calculation in all range of polynomial definition are discussed. These difficulties are illustrated on results of computing the Hahn polynomials. The stability of computational schemes with reference to round-off errors is investigated. Stable method of calculation is proposed. The calculations of Hahn and $q$-Hahn polynomials are carried out with fine accuracy.