Remark on a Mittag–Leffler function of Le Roy type

Abstract

We give some necessary and some sufficient conditions for the complete monotonicity on the negative half-line of a Mittag–Leffler function of Le Roy type. It is conjectured that the underlying positive random variable, when it exists, must be logarithmically infinitely divisible.

Keywords:

• Complete monotonicity
• gamma function
• infinite divisibility
• Le Roy function
• Mittag–Leffler function

AMS CLASSIFICATIONS:

• 33E12
• 60E10

Disclosure statement

No potential conflict of interest was reported by the author(s).