A converse to the neo-classical inequality ...
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
A converse to the neo-classical inequality with an application to the Mittag-Leffler function
Author(s) :
Gerhold, Stefan [Auteur]
Vienna University of Technology = Technische Universität Wien [TU Wien]
Simon, Thomas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Vienna University of Technology = Technische Universität Wien [TU Wien]
Simon, Thomas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Journal title :
Monatshefte für Mathematik
Pages :
627-645
Publisher :
Springer Verlag [1948-....]
Publication date :
2023-01-14
ISSN :
0026-9255
English keyword(s) :
Mittag-Leffler function
Log-convexity
Stable subordinator
Binomial coefficient
Log-convexity
Stable subordinator
Binomial coefficient
HAL domain(s) :
Mathématiques [math]
English abstract : [en]
We prove two inequalities for the Mittag-Leffler function, namely that the function $\log E_\alpha (x^\alpha )$ is sub-additive for $0<\alpha <1,$ and super-additive for $\alpha >1.$ These assertions follow from two new ...
Show more >We prove two inequalities for the Mittag-Leffler function, namely that the function $\log E_\alpha (x^\alpha )$ is sub-additive for $0<\alpha <1,$ and super-additive for $\alpha >1.$ These assertions follow from two new binomial inequalities, one of which is a converse to the neo-classical inequality. The proofs use a generalization of the binomial theorem due to Hara and Hino (Bull London Math Soc 2010). For $0<\alpha <2,$ we also show that $E_\alpha (x^\alpha )$ is log-concave resp. log-convex, using analytic as well as probabilistic arguments.Show less >
Show more >We prove two inequalities for the Mittag-Leffler function, namely that the function $\log E_\alpha (x^\alpha )$ is sub-additive for $0<\alpha <1,$ and super-additive for $\alpha >1.$ These assertions follow from two new binomial inequalities, one of which is a converse to the neo-classical inequality. The proofs use a generalization of the binomial theorem due to Hara and Hino (Bull London Math Soc 2010). For $0<\alpha <2,$ we also show that $E_\alpha (x^\alpha )$ is log-concave resp. log-convex, using analytic as well as probabilistic arguments.Show less >
Language :
Anglais
Popular science :
Non
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