Limit relationships between Chebyshev and Hahn polynomials (Q1842444)

In the paper the convergence of Hahn polynomials with parameters \(\alpha= \beta= -1/2\) or \(\alpha= \beta= 1/2\) to Chebyshev polynomials of the first or second kind, respectively, is investigated. Exact bounds in various metrics are proved for the difference between the Chebyshev polynomials and the corresponding Hahn polynomials. Besides of that recurrence relations are obtained for the expansion coefficients of polynomials in a discrete argument by polynomials in a continuous one.