Asymptotic properties and weighted estimates for Chebyshev--Hahn orthogonal polynomials
Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 387-401
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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.
@article{SM_1992_72_2_a6,
author = {I. I. Sharapudinov},
title = {Asymptotic properties and weighted estimates for {Chebyshev--Hahn} orthogonal polynomials},
journal = {Sbornik. Mathematics},
pages = {387--401},
publisher = {mathdoc},
volume = {72},
number = {2},
year = {1992},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1992_72_2_a6/}
}
I. I. Sharapudinov. Asymptotic properties and weighted estimates for Chebyshev--Hahn orthogonal polynomials. Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 387-401. http://geodesic.mathdoc.fr/item/SM_1992_72_2_a6/