Geodesic
A bound on the Laguerre polynomials
Studia Mathematica, Tome 100 (1991) no. 2, pp. 169-181

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We give the following bounds on Laguerre polynomials and their derivatives (α ≥ 0): $|t^k d^p (L_n^α(t) e^{-t/2})| ≤ 2^{-min(α,k)} 4^k(n + 1)...(n + k) ({n + p + max(α - k, 0)} \atop {n})$ for all natural numbers k, p, n ≥ 0 and t ≥ 0. Also, we give (as the main result of this paper) a technique to estimate the order in k and p in bounds similar to the previous ones, which will be used to see that the estimate on k and p in the previous bounds is sharp and to give an estimate on k and p in other bounds on the Laguerre polynomials proved by Szegö.
DOI : 10.4064/sm-100-2-169-181
Keywords: Laguerre polynomials

Antonio J. Duran 1

1 
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Antonio J. Duran. A bound on the Laguerre polynomials. Studia Mathematica, Tome 100 (1991) no. 2, pp. 169-181. doi: 10.4064/sm-100-2-169-181

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