A complete monotonicity property of the gamma function

被引：144

作者：

Qi, F ^{[1
]}

Chen, CP ^{[1
]}

机构：

[1] Jiaozuo Inst Technol, Dept Appl Math & Informat, Henan 454000, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2004年 / 296卷 / 02期

基金：

美国国家科学基金会;

关键词：

gamma function; psi function; logarithmically completely monotonic function;

D O I：

10.1016/j.jmaa.2004.04.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A logarithmically completely monotonic function is completely monotonic. The function 1 - lnx +1/x ln Gamma(x + 1) is strictly completely monotonic on (0, infinity). The function (x)rootGamma(x+1)/x is strictly logarithmically completely monotonic on (0, infinity). (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：603 / 607

页数：5

共 16 条

[1]

CHEN CP, 2003, J INEQUAL PURE APPL, V3

[2]

CHEN CP, 2002, RES REP COLL, V5

[3] The best bounds in Gautschi's inequality [J].

Elezovic, N ;

Giordano, C ;

Pecaric, J .

MATHEMATICAL INEQUALITIES & APPLICATIONS, 2000, 3 (02) :239-252

[4] ERROR-BOUNDS FOR ASYMPTOTIC EXPANSIONS OF THE RATIO OF 2 GAMMA-FUNCTIONS [J].

FRENZEN, CL .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1987, 18 (03) :890-896

[5]

Guo BN, 2001, MATH INEQUAL APPL, V4, P195

[6]

GUO BN, 1999, RGMIA RES REP, V2, P1059

[7]

KERSHAW D, 1985, ATTI ACCAD SCI TORIN, V119, P127

[8]

Magnus W., 1966, FORMULAS THEOREMS SP

[9] Note on monotonicity of generalized weighted mean values [J].

Qi, F ;

Zhang, SQ .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1999, 455 (1989) :3259-3260

[10] Generalized weighted mean values with two parameters [J].

Qi, F .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1998, 454 (1978) :2723-2732

← 1 2 →