SHARP GAUTSCHI INEQUALITY FOR PARAMETER 0 < p < 1 WITH APPLICATIONS

被引：49
作者：
Yang, Zhen-Hang [1 ]
Zhang, Wen [2 ]
Chu, Yu-Ming [1 ]
机构：
[1] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China
[2] Icahn Sch Med Mt Sinai, Friedman Brain Inst, New York, NY 10029 USA
来源：
MATHEMATICAL INEQUALITIES & APPLICATIONS | 2017年 / 20卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Incomplete gamma function; gamma function; psi function; INCOMPLETE GAMMA-FUNCTION; UNIFORM ASYMPTOTIC-EXPANSION; FUNCTIONAL INEQUALITIES; BOUNDS; MONOTONICITY; ERROR; INTEGRALS; FORMULAS;
D O I：
10.7153/mia-2017-20-71
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the article, we present the best possible parameters a,b on the interval ( 0,8) such that the Gautschi double inequality [(x(p) + a)(1/p) - x]/a < e(xp) integral(8)(x) e(-tp) dt < [(x(p) + b)(1/p) - x]/b holds for all x > 0 and p is an element of(0,1). As applications, we find new bounds for the incomplete gamma function Gamma(a, x) = integral(8)(x) t(a-1) e(-t) dt.
引用
收藏
页码：1107 / 1120
页数：14
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