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.
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页码：329 / 341
页数：13
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