4th order Pade approximation of the inverse single parameter Mittag-Leffler Function

4th order Pade approximation of the inverse single parameter Mittag-Leffler Function

4th order Pade approximation of the inverse single parameter Mittag-Leffler Function ,$L_{\alpha}(y)$ where the input scaler or vector,y, is positive and $0.05< \alpha <= 1$. The 4th order polynomial coefficients lookup table is provided in the Matlab data file 'E_a_4th_order_coefficients.mat' which needs to be loaded in your workspace to gives the parameter array variable called 'E_a_4th_order_coefficients'. The four expressions to evaluate the roots of the inverse Pade approximation are are in the Matlab data file 'L_a_fx.mat' which needs to be loaded in your workspace to give the parameter array variable called 'L_a_fx'. The code selects the expression which produces a root which is negative and real for the specific values of alpha and (y,a0,p1,p2,p3,q0,q1,q2,q3). The coefficients in the table are calculated for alpha values with precision of 0.001. For input alpha values that are specified with greater precision, the polynomial coefficients will be calculated by interpolation.
(C) 2015 Carson Ingo & Thomas R. Barrick