Summary
We investigate the asymptotic behaviour of ℒ n (n),n→∞ where ℒ n (x) denotes the Laguerre polynomial of degreen. Our results give a partial answer to the conjecture ∣ℒ 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\(6\sqrt {{3 \mathord{\left/ {\vphantom {3 \pi }} \right. \kern-\nulldelimiterspace} \pi }} \).
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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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Elbert, A., Laforgia, A. & Rodono, L.G. Asymptotics for thenth-degree Laguerre polynomial evaluated atn . Numer. Math. 63, 173–182 (1992). https://doi.org/10.1007/BF01385854
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DOI: https://doi.org/10.1007/BF01385854