Some classes of completely monotonic functions, II

被引：56

作者：

Alzer, Horst ^{[1
]}

Berg, Christian ^{[1
]}

机构：

[1] Univ Copenhagen, Dept Math, DK-2100 Copenhagen, Denmark

来源：

RAMANUJAN JOURNAL | 2006年 / 11卷 / 02期

关键词：

complete monotonicity; gamma; digamma and polygamma functions; Prime numbers; inequalities;

D O I：

10.1007/s11139-006-6510-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A function f : (0, oo) R is said to be completely monotonic if (-1)(n) f((n))(X) >= 0 for all x > 0 and n = 0, 1, 2,. In this paper we present several new classes of completely monotonic functions. Our functions have in common that they are defined in terms of the classical gamma, digamma, and polygamma functions. Moreover, we apply one of our monotonicity theorems to prove a new inequality for prime numbers. Some of the given results extend and complement theorems due to Bustoz & Ismail, Clark & Ismail, and other researchers.

引用

页码：225 / 248

页数：24

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