Some Properties of the Kilbas-Saigo Function
Lotfi Boudabsa
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.
Topics & Concepts
Monotonic functionSubordinatorFunction (biology)MathematicsRepresentation (politics)Probabilistic logicPure mathematicsApplied mathematicsMathematical analysisStatisticsPolitical scienceEvolutionary biologyLawLévy processPoliticsBiologyMathematical functions and polynomialsMathematical Inequalities and ApplicationsMathematics and Applications