Some Properties of the Kilbas-Saigo Function

被引：20

作者：

Boudabsa, Lotfi ^{[1
]}

Simon, Thomas ^{[2
]}

机构：

[1] Ecole Polytech Fed Lausanne, Inst Math, CH-1015 Lausanne, Switzerland

[2] Univ Lille, Lab Paul Painleve, UMR 8524, Cite Sci, F-59655 Villeneuve Dascq, France

来源：

MATHEMATICS | 2021年 / 9卷 / 03期

关键词：

complete monotonicity; convex ordering; double Gamma function; fractional extreme distribution; Kilbas-Saigo function; Le Roy function; Mittag-Leffler function; stable subordinator; LEFFLER; ASYMPTOTICS;

D O I：

10.3390/math9030217

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize the complete monotonicity of the Kilbas-Saigo function on the negative half-line. We also provide the exact asymptotics at -infinity, and uniform hyperbolic bounds are derived. The same questions are addressed for the classical Le Roy function. The main ingredient for the proof is a probabilistic representation of these functions in terms of the stable subordinator.

引用

页码：1 / 24

页数：24

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