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]

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

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 >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL