Finite series representation of the inverse Mittag-Leffler function
type: Item
instance of: scholarly article
title: Finite series representation of the inverse Mittag-Leffler function
zbMATH Open document ID: 1407.33018
DOI: 10.1155/2014/252393
author: J. W. Hanneken
author: B. N. N. Achar
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: The inverse Mittag-Leffler function \(E_{\alpha, \beta}^{- 1} \left(z\right)\) 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 \(\alpha\) and \(\beta\); specifically, \(0 < \alpha < 1 / 2\) for \(\beta = 1\) and for \(\beta = 2\). 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.
Mathematics Subject Classification ID: 33E12
Mathematics Subject Classification ID: 33F05
zbMATH DE Number: 7015998
Wikidata QID: Q59065081
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/252393
OpenAlex ID: W2043375358
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description: scientific article; zbMATH DE number 7015998