We give the following bounds on Laguerre polynomials and their derivatives (α ≥ 0): 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.
@article{bwmeta1.element.bwnjournal-article-smv100i2p169bwm,
author = {Antonio Duran},
title = {A bound on the Laguerre polynomials},
journal = {Studia Mathematica},
volume = {100},
year = {1991},
pages = {169-181},
zbl = {0734.33003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv100i2p169bwm}
}
Duran, Antonio. A bound on the Laguerre polynomials. Studia Mathematica, Tome 100 (1991) pp. 169-181. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv100i2p169bwm/
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