Combining arbitrary order global Pad\'e approximation of the Mittag-Leffler function with its addition formula for a significant accuracy boost

The combination of the global Pad\'e approximation of the Mittag-Leffler function with its addition formula for the case α<1 yields significantly higher accuracy results for a given arbitrary order n. We present a solution in terms of a Mathematica notebook to determine the general structure of the system of linear equations to be solved, followed by an implementation as a {{C++}} program using the {{Eigen}} template library for linear algebra. For a comparison with contour integral solutions we present an implementation as a {{C++}} program using the {{boost}} library's quadrature package employing the Gauss-Kronrod-method.