Finite Series Representation of the Inverse Mittag-Leffler Function

Abstract EN

The inverse Mittag-Leffler function Eα,β-1z is valuable in determining the value of the argument of a Mittag-Leffler function given the value of the function and it is not an easy problem.

A finite series representation of the inverse Mittag-Leffler function has been found for a range of the parameters α and β; specifically, 0<α<1/2 for β=1 and for β=2.

This finite series representation of the inverse Mittag-Leffler function greatly expedites its evaluation and has been illustrated with a number of examples.

This represents a significant advancement in the understanding of Mittag-Leffler functions.