Uniform bounds for the complementary incomplete gamma function

Title: Uniform bounds for the complementary incomplete gamma function
Creator: Borwein, Jonathan M.; Chan, O-yeat
Relation: Mathematical Inequalities and Applications Vol. 12, Issue 1, p. 115-121
Publisher Link: http://dx.doi.org/10.7153/mia-12-10
Publisher: Element d.o.o.
Resource Type: journal article
Date: 2009
Description: We prove upper and lower bounds for the complementary incomplete gamma function Г(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, |Г(a, z)| is of order |z|^a−1e^−Re(z), and extends an upper estimate of Natalini and Palumbo to complex values of z.
Subject: incomplete gamma function; inequalities; uniform bounds
Identifier: http://hdl.handle.net/1959.13/940194
Identifier: uon:12968
Identifier: ISSN:1331-4343
Language: eng
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