Sums of the Powers of the Zeros of the Mittag-Leffler Function
Abstract
The Mittag-Leffler function, which is a generalization of the exponential function, occurs naturally in the solution of dynamic problems involving fractional calculus. For example see the book Fractional Differential Equations by Podlubny, or for a specific application see the problem of the fractional oscillator by Achar et. al. Physica A297 (2001) 361 and A309 (2002) 275. The zeros of the Mittag-Leffler function play a significant role in the dynamic solutions. However, very little is known about these zeros. A summary of the available information about the zeros of Mittag-Leffler functions will be given and new results pertaining to the sums of the powers of the zeros will be presented.
- Publication:
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APS March Meeting Abstracts
- Pub Date:
- March 2004
- Bibcode:
- 2004APS..MARY38008H