Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 47, Issue 1, Pages 69-88Publisher
SIAM PUBLICATIONS
DOI: 10.1137/070700280
Keywords
special functions of mathematical physics; fractional calculus; generalized Mittag-Leffler functions; numerical algorithms
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A numerical algorithm for calculating the generalized Mittag-Leffler E alpha, beta(z) function for arbitrary complex argument z and real parameters alpha > 0 and beta is an element of R 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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