- Tytuł:
- A bound on the Laguerre polynomials
- Autorzy:
- Duran, Antonio J.
- Powiązania:
- https://bibliotekanauki.pl/articles/1293522.pdf
- Data publikacji:
- 1991
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
- Laguerre polynomials
- Opis:
- 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.
- Źródło:
-
Studia Mathematica; 1991, 100, 2; 169-181
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł