Uniform bounds for the complementary incomplete gamma function, Preprint at http://locutus.cs.dal.ca:8088/archive/00000335
by
Jonathan M. Borwein
,
O-yeat Chan
| Citations: | 1 - 1 self |
BibTeX
@MISC{Borwein_uniformbounds,
author = {Jonathan M. Borwein and O-yeat Chan},
title = {Uniform bounds for the complementary incomplete gamma function, Preprint at http://locutus.cs.dal.ca:8088/archive/00000335},
year = {}
}
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Abstract
Abstract. We prove upper and lower bounds for the complementary incomplete gamma function Γ(a, z) with complex parameters a and z. Our bounds are refined within the circular hyperboloid of one sheet {(a, z) : |z |> c|a − 1|} with a real and z complex. Our results show that within the hyperboloid, |Γ(a, z) | is of order |z | a−1 e − Re(z) , and extends an upper estimate of Natalini and Palumbo to complex values of z.
Citations
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| 2 | Effective Laguerre asymptotics, Preprint available at http://locutus.cs.dal.ca:8088/archive/00000334 - Borwein, Borwein, et al. |
| 2 | A uniform asymptotic expansion for the incomplete gamma function - Paris |
