The Mittag-Leffler function is computed via a quadrature approximation of a contour integral representation. We compare results for parabolic and hyperbolic contours, and give special attention to evaluation on the real line. The main point of difference with respect to similar approaches from the literature is the way that poles in the integrand are handled. Rational approximation of the Mittag-Leffler function on the negative real axis is also discussed.

中文翻译：

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Mittag-Leffler函数的数值评估

Mittag-Leffler函数是通过轮廓积分表示的正交近似来计算的。我们比较抛物线轮廓和双曲线轮廓的结果，并特别注意实线上的评估。与文献中类似方法相比，主要区别在于处理被积物中极点的方式。还讨论了Mittag-Leffler函数在负实轴上的有理逼近。