LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS INVOLVING GENERALIZED GAMMA AND q- GAMMA FUNCTIONS

被引：0

作者：

Krasniqi, Valmir ^{[1
]}

Guo, Senlin ^{[2
]}

机构：

[1] Univ Prishtina, Dept Math, Prishtine 10000, Pristina, Kosovo

[2] Zhongyuan Univ Tech, Zhengzhou 450007, Henan, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND SPECIAL FUNCTIONS | 2010年 / 1卷 / 02期

关键词：

Completely monotonic function; logarithmically completely monotonic function; Gamma function; Psi function; inequality;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove that the function f(alpha,beta,p) (x) = Gamma(p()x vertical bar beta)/p(x)x(x)+beta-alpha(x+p)(x+p+beta-alpha) is logarithmically completely monotonic on (0, infinity) if 2 alpha <= 1 <= beta, and the function g(m,alpha) (x) = x(alpha) (vertical bar psi((m))(p) (x)vertical bar - ((m-1)!)(xm) vertical bar (m(m-1)!)((x vertical bar p))) is strictly completely monotonic on (0, infinity) fora <= 1.

引用

页码：8 / 16

页数：9

共 18 条

[1]

Abramowitz M., 1965, HDB MATH FUNCT FORMU

[2]

Askey R., 1978, APPL ANAL, V8, P125, DOI [10.1080/00036817808839221, DOI 10.1080/00036817808839221]

[3]

BOCHER S, 2005, HARMONIC ANAL THEORY

[4]

Bullen P. S., 2003, MATH APPL, V560

[5]

Chen Ch.-P., 2006, GEN MATH, V14, P127

[6] Logarithmically completely monotonic functions relating to the gamma function [J].

Chen, Chao-Ping ;

Qi, Feng .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 321 (01) :405-411

[7]

Ismail M. E. H., 1994, APPROXIMATION COMPUT, V119, P309, DOI DOI 10.1007/978-1-4684-7415-2_

[8] On a q-analogue of the p-adic log gamma functions and related integrals [J].

Kim, T .

JOURNAL OF NUMBER THEORY, 1999, 76 (02) :320-329

[9]

Kim T., 2000, ADV STUD CONT MATH, V2, P37

[10]

KIM T, 2004, ADV STUD CONT MATH, V8, P111

← 1 2 →