Boudabsa, LotfiSimon, Thomas2021-03-262021-03-262021-03-262021-02-0110.3390/math9030217https://infoscience.epfl.ch/handle/20.500.14299/176566WOS:000615416100001We 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.Mathematicscomplete monotonicityconvex orderingdouble gamma functionfractional extreme distributionkilbas-saigo functionle roy functionmittag-leffler functionstable subordinatortext::journal::journal article::research article