The calculation of the Mittag-Leffler function

The problem of calculating the Mittag-Leffler function E-rho,E-mu (z) is considered in the paper. To solve this problem integral representations for the function E-rho,E-mu(z) are transformed in such a way that they could not contain complex variables and parameters. Integral representations written in this form allow one to use standard methods of numerical integration to calculate integrals contained in them. To verify the correctness of the integral representations obtained the function E-rho,E-mu (z) was calculated both with the use of obtained formulas and with the use of known representations of the MittagLeffler function. The calculation results demonstrate their exact matching. This fact is indicative of the correctness of new integral representations of the function E-rho,E-mu(z) that were obtained.