PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 70(84), pp. 2636 (2001) 

Orthogonal polynomials and regularly varying sequencesSlavko Simi\'cMatemati\v cki institut SANU, Kneza Mihaila 35, 11000 Beograd, p.p. 367, YugoslaviaAbstract: We introduce a method of estimating asymptotic behaviour of polynomials $Q_n^{(\alpha)}(x):=\sum_{k\le n}c_k a_{nk} x^k$, $n\to\infty$, related to a given polynomial $Q_n(x):=\sum_{k\le n} a_{nk}x^k$, where $(c_k)$, $k\in N$ is any regularly varying sequence of index $\alpha$ in the sense of Karamata. Then we apply our results to classical orthogonal polynomials as relevant examples. Classification (MSC2000): 42C05; 26A12 Full text of the article:
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