Mathematics Special Functions

Numerical Algorithm for Calculating the Generalized Mittag-Leffler Function

H.J. Seybold, R. Hilfer

SIAM Journal on Numerical Analysis 47, 69 (2008)

submitted on
Saturday, August 16, 2008

A numerical algorithm for calculating the generalized Mittag-Leffler function for arbitrary complex argument and real parameters is presented. The algorithm uses the Taylor series, the exponentially improved asymptotic series, and integral representations to obtain optimal stability and accuracy of the algorithm. Special care is applied to the limits of validity of the different schemes to avoid instabilities in the algorithm.

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