A monotonicity property of the Mittag-Leffler function

Alzer, Horst and Kwong, Man Kam: A monotonicity property of the Mittag-Leffler function. In: Acta scientiarum mathematicarum, (85) 1-2. pp. 181-187. (2019)

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Let Fα,β(x) = βEβ(x ) − αEα(x ), where Eα denotes the Mittag– Leffler function. We prove that if α, β ∈ (0, 1], then Fα,β is completely monotonic on (0, ∞) if and only if α ≤ β. This extends a result of T. Simon, who proved in 2015 that Fα,1 is completely monotonic on (0, ∞) if α ∈ (0, 1]. Moreover, we apply our monotonicity theorem to obtain some functional inequalities involving Fα,β.

Item Type: Article
Journal or Publication Title: Acta scientiarum mathematicarum
Date: 2019
Volume: 85
Number: 1-2
ISSN: 2064-8316
Page Range: pp. 181-187
Official URL: http://www.acta.hu
DOI: https://doi.org/10.14232/actasm-018-263-5
Uncontrolled Keywords: Matematika
Additional Information: Bibliogr.: 187. p. ; összefoglalás angol nyelven
Date Deposited: 2019. Sep. 25. 10:21
Last Modified: 2019. Sep. 25. 10:21
URI: http://acta.bibl.u-szeged.hu/id/eprint/62140

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