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arXiv · 2012.05666

Some properties of the Kilbas-Saigo function

Lotfi Boudabsa·Thomas Simon
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Abstract

We characterize the complete monotonicity of the Kilbas-Saigo function on the negative half-line. We also provide the exact asymptotics at $-\infty$, 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.

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Lotfi Boudabsa, Thomas Simon. 2020-12-10. Some properties of the Kilbas-Saigo function. https://arxiv.org/abs/2012.05666

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