UNIFORM BOUNDS FOR THE COMPLEMENTARY INCOMPLETE GAMMA FUNCTION

被引：24

作者：

Borwein, Jonathan M. ^{[1
]}

Chan, O-Yeat ^{[2
]}

机构：

[1] Dalhousie Univ, Fac Comp Sci, Halifax, NS B3H 1W5, Canada

[2] Dalhousie Univ, Dept Math & Stat, Halifax, NS B3H 1W5, Canada

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2009年 / 12卷 / 01期

关键词：

Incomplete Gamma Function; Inequalities; Uniform Bounds; INEQUALITIES;

D O I：

10.7153/mia-12-10

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove upper and lower bounds for the complementary incomplete gamma function Gamma(a, z) with complex parameters a and z. Our bounds are refined within the circular hyperboloid of one sheet {(a, z) : vertical bar z vertical bar > c vertical bar a - 1 vertical bar} with a real and z complex. Our results show that within the hyperboloid, vertical bar Gamma(a, z)vertical bar is of order vertical bar Z vertical bar(a-1)e(-Re(z)), and extends an upper estimate of Natalini and Palumbo to complex values of z.

引用

页码：115 / 121

页数：7

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