An Alpha-Beta Phase Diagram Representation of the Zeros and Properties of the Mittag-Leffler Function

Hanneken John W<sup>*</sup>; Achar B N Narahari; Vaught David M

doi:10.1155/2013/421685

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An Alpha-Beta Phase Diagram Representation of the Zeros and Properties of the Mittag-Leffler Function

作者：Hanneken John W^*; Achar B N Narahari; Vaught David M

来源：Advances in Mathematical Physics, 2013, 2013: 421685.

DOI：10.1155/2013/421685

摘要

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,E-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.