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Polynomials defined on a discrete set of points or, in other words, polynomials of a discrete argument are used in many parts of mathematics, in particular in function approximation theory, and also in theoretical physics [1, 2]. One of the basic tools for the analysis of polynomials of a discrete argument is the establishment of asymptotic equality to corresponding polynomials of a continuous argument (i.e., polynomials orthogonal on a continuum of points). This approach to the study of discrete polynomials has been implemented by a number of authors. Convergence of Hahn polynomials of a discrete argument to classical Jacobi polynomials is studied in [2][3][4][5]. In this paper, we consider the convergence of Hahn polynomials with the parameters a = /3 = --1/2 and a = /3 = 1/2 to Chebyshev polynomials of the first and second kind, respectively. In distinction from [4, 5], we derive exact bounds for the difference of Chebyshev polynomials and the corresponding Hahn polynomials in various metrics and obtain recurrences for the expansion coefficients of arbitrary polynomials of a discrete argument by polynomials of a continuous argument.We start with some def'mitions.

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