Some Properties of the Kilbas-Saigo Function

Lotfi Boudabsa and Thomas Simon
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Lotfi Boudabsa: Institut de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
Thomas Simon: Laboratoire Paul Painlevé, UMR 8524, Université de Lille, Cité Scientifique, F-59655 Villeneuve d’Ascq, France

Mathematics, 2021, vol. 9, issue 3, 1-24

Abstract: We characterize the complete monotonicity of the Kilbas-Saigo function on the negative half-line. We also provide the exact asymptotics at ? ? , 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.

Keywords: complete monotonicity; convex ordering; double Gamma function; fractional extreme distribution; Kilbas-Saigo function; Le Roy function; Mittag–Leffler function; stable subordinator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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