An alpha-beta phase diagram representation of the zeros and properties of the Mittag-Leffler function (Q2248430)

Summary: A significant advance in characterizing the nature of the zeros and organizing the Mittag-Leffler functions into phases according to their behavior is presented. Regions have been identified in the domain of \(\alpha\) and \(\beta\) where the Mittag-Leffler functions \(E_{\alpha,\beta}(z)\) have not only the same type of zeros but also exhibit similar functional behavior, and this permits the establishment of an \(\alpha-\beta\) phase diagram.