Some Properties of the Kilbas-Saigo Function

By Lotfi Boudabsa, Thomas Simon. Mathematics, 2020

51 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/cd2fcbd85087c7da7f5af580615920a2cdbe4e0e