A+ CATEGORY SCIENTIFIC UNIT

A bound on the Laguerre polynomials

Volume 100 / 1991

Antonio J. Duran Studia Mathematica 100 (1991), 169-181 DOI: 10.4064/sm-100-2-169-181

Abstract

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.

Authors

  • Antonio J. Duran

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