Asymptotic properties and weighted estimates for Chebyshev–Hahn orthogonal polynomials

The asymptotic behavior is investigated for the classical Chebyshev–Hahn orthogonal polynomials $Q_n(x;\alpha,\beta,N)$ $(0\leqslant n\leqslant N-1)$, which form an orthogonal system on the set $\{0,1\dots,N-1\}$ with the weight
$$ \rho(x)=c\frac{\Gamma(x+\alpha+1)\Gamma(N-x+\beta)}{\Gamma(x+1)\Gamma(N-x)} \quad (\alpha,\beta>-1) $$
and are such that $Q_n(0,\alpha,\beta,N)=1$. A weighted estimate is established as a corollary.