Evaluation of the Mittag-Leffler Function

Abstract: 

Although Mittag-Leffler introduced his namesake function over 115 years ago, it never played a role in applications until the 1990s and so was never included in the standard numerical libraries for special functions.  Several approaches based on contour integral

representations have been developed over the past 18 years.  I will describe a modification of a method of Weideman and Trefethen for the case of most importance for applications.  This modification leads to a highly accurate rational approximation.