Mittag-Leffler functions and complete monotonicity

Abstract

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 previous works by various authors.

Keywords:

• Abelian transform
• complete monotonicity
• incomplete Gamma function
• Mellin transform
• Mittag-Leffler function
• Stieltjes transform

Mathematics Subject Classification:

• 26A33
• 26A48
• 33E12
• 60G52