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.

arXiv comment22 pages, 19 figures

References in corpus (5)

• The AAA algorithm for rational approximation
• Numerical evaluation of two and three parameter Mittag-Leffler functions
• The Mittag-Leffler function
• Global Padé approximations of the generalized Mittag-Leffler function and its inverse
• Asymptotics of the Mittag-Leffler function $E_a(z)$ on the negative real axis when $a\to 1$

Cited by in corpus (3)

• A contour method for time-fractional PDEs and an application to fractional viscoelastic beam equations
• Analyses of the contour integral method for time fractional subdiffusion-normal transport equation
• Exponentially Convergent Numerical Method for Abstract Cauchy Problem with Fractional Derivative of Caputo Type