Finite Series Representation of the Inverse Mittag-Leffler Function. (25th March 2014)

• Record Type: Journal Article
• Authors: Hanneken, John W.; Achar, B. N. Narahari
• Other Names: Tenreiro Machado J. A. Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2014(2014)
• Publication Date: 2014-03-25
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2014/252393
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : The inverse Mittag-Leffler function E α, β - 1 z 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.