Asymptotics for thenth-degree Laguerre polynomial evaluated atn |
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| Authors: | Arpad Elbert Andrea Laforgia Lucia G Rodono |
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| Institution: | (1) Mathematical Institute of the Hungarian Academy of Sciences, P.O.B. 127, H-1364 Budapest, Hungary;(2) Dipartimento di Matematica, Via N. Sauro 85, I-85100 Potenza, Italy;(3) Dipartimento di Matematica ed Applicazioni, Università degli Studi di Palermo, Via Archirafi 34, I-90123 Palermo, Italy |
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| Abstract: | Summary We investigate the asymptotic behaviour of 
n
(n),n  where
n
(x) denotes the Laguerre polynomial of degreen. Our results give a partial answer to the conjecture 
n
(n)>1 forn>6, made in 1984 by van Iseghem. We also show the connection between this conjecture and the continued fraction approximants of
.Work sponsored by the Consiglio Nazionale delle Ricerche and by the Ministero dell'Università e della Ricerca Scientifica e Tecnologica of Italy |
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| Keywords: | 33A65 41A60 41A21 |
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