Numerical evaluation of Mittag-Leffler functions

Abstract

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.

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Correspondence to William McLean.

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McLean, W. Numerical evaluation of Mittag-Leffler functions. Calcolo 58, 7 (2021). https://doi.org/10.1007/s10092-021-00398-6

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Keywords

  • Special functions
  • Fractional calculus
  • Quadrature
  • Contour integration
  • Rational approximation

Mathematics Subject Classification

  • 33F05
  • 41A20
  • 65D32