A Completely Monotonic Function Used in an Inequality of Alzer

被引：4

作者：

Berg, Christian ^{[1
]}

Pedersen, Henrik L. ^{[2
]}

机构：

[1] Univ Copenhagen, Inst Math Sci, DK-2100 Copenhagen O, Denmark

[2] Univ Copenhagen, Dept Basic Sci & Environm, DK-1871 Frederiksberg C, Denmark

来源：

COMPUTATIONAL METHODS AND FUNCTION THEORY | 2012年 / 12卷 / 01期

关键词：

Completely monotonic function; Stieltjes transform; GAMMA-FUNCTION;

D O I：

10.1007/BF03321830

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The function G(x) = (1 - ln(x)/ln(1 + x))x ln(x) has been considered by Alzer and by Qi and Guo. We prove that G' is completely monotonic by finding an integral representation of the holomorphic extension of G to the cut plane. A main difficulty is caused by the fact that G' is not a Stieltjes transform.

引用

页码：329 / 341

页数：13

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