Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

A bound on the Laguerre polynomials

100%

Duran A. J.

Studia Mathematica

1991

tom 100

nr 2

169-181

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.

Ograniczanie wyników

1 Studia Mathematica

1 Duran A. J.

1 1991

Wyniki wyszukiwania

A bound on the Laguerre polynomials