Sums of the Powers of the Zeros of the MittagLeffler Function
Abstract
The MittagLeffler 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 MittagLeffler 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 MittagLeffler functions will be given and new results pertaining to the sums of the powers of the zeros will be presented.
 Publication:

APS March Meeting Abstracts
 Pub Date:
 March 2004
 Bibcode:
 2004APS..MARY38008H