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Finite Series Representation of the Inverse Mittag-Leffler Function

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  • John W. Hanneken
  • B. N. Narahari Achar

Abstract

The inverse Mittag-Leffler function 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 and ; specifically, for and for . 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.

Suggested Citation

  • John W. Hanneken & B. N. Narahari Achar, 2014. "Finite Series Representation of the Inverse Mittag-Leffler Function," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-18, March.
    • Handle: RePEc:hin:jnlmpe:252393
    DOI: 10.1155/2014/252393
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