Geodesic
Orthogonal Polynomials and Regularly Varying Sequences
Publications de l'Institut Mathématique, _N_S_70 (2001) no. 84, p. 26

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 : 42C05 26A12 
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     author = {Slavko Simi\'c},
     title = {Orthogonal {Polynomials} and {Regularly} {Varying} {Sequences}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {26 },
     publisher = {mathdoc},
     volume = {_N_S_70},
     number = {84},
     year = {2001},
     zbl = {1034.42025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2001_N_S_70_84_a3/}
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Slavko Simić. Orthogonal Polynomials and Regularly Varying Sequences. Publications de l'Institut Mathématique, _N_S_70 (2001) no. 84, p. 26 . http://geodesic.mathdoc.fr/item/PIM_2001_N_S_70_84_a3/