Completely monotonic functions

被引：221

作者：

Miller, KS ^{[1
]}

Samko, SG ^{[1
]}

机构：

[1] Univ Algarve, Unidad Ciencias Exactas, P-8000 Faro, Portugal

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2001年 / 12卷 / 04期

基金：

美国国家科学基金会;

关键词：

completely monotonic functions; integral transforms; infinitely divisible probability distributions;

D O I：

10.1080/10652460108819360

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this expository article we survey some properties of completely monotonic functions and give various examples, including some famous special functions. Such function are useful, for example, in probability theory. It is known, [1, p.450], for example, that a function omega is the Laplace transform of an infinitely divisible probability distribution on (0, infinity), if and only if omega = e(-h), where the derivative of h is completely monotonic and h(0+) = 0.

引用

页码：389 / 402

页数：14

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