Mittag-Leffler functions and complete monotonicity

Thomas Simon (1, 2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

We consider two operations on the Mittag-Leffler function which cancel the exponential term in the expansion at infinity, and generate a completely monotonic function. The first one is the action of a certain differential-difference operator, and leads to a characterization via some necktie domain. The second one is the subtraction of the exponential term itself multiplied by an incomplete Gamma function. These results extend and generalize previous works by various authors.

Mots clés: Abelian transform; Complete monotonicity; Incomplete Gamma function; Mellin transform; Mittag-Leffler function; Stable process; Stieltjes transform.; Stieltjes transform

Domaines: Analyse classique [math.CA]; Probabilités [math.PR]

Thomas Simon. Mittag-Leffler functions and complete monotonicity. 2013. ⟨hal-00919021v1⟩