Some properties of the Kilbas-Saigo function

2020/12/10 by Boudabsa, Lotfi, Simon, Thomas · 2 citations
#33E12 (Primary) 33B15 #60E15 #60G52 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2012.05666

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.

Cited by

• Mittag-Leffler functions and convex ordering
• A Generalization of the Fox H-function

Related

• Remark on a Mittag-Leffler function of Le Roy type
• Sharp quantitative Faber-Krahn inequalities and the Alt-Caffarelli-Friedman monotonicity formula
• Explicit Upper Bounds for L-functions on the critical line
• Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function
• Fractional extreme distributions