Asymptotics of orthogonal polynomials in a~neighborhood of the~endpoints of the~interval of orthogonality
Sbornik. Mathematics, Tome 76 (1993) no. 1, pp. 35-50

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The well-known Mehler–Heine asymptotic formula for the classical Jacobi polynomials is extended to broader classes of orthogonal polynomials.
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A. I. Aptekarev. Asymptotics of orthogonal polynomials in a~neighborhood of the~endpoints of the~interval of orthogonality. Sbornik. Mathematics, Tome 76 (1993) no. 1, pp. 35-50. http://geodesic.mathdoc.fr/item/SM_1993_76_1_a2/