mlpade

MATLAB functions for Pade approximations of the Mittag-Leffler function, E_α,β(-x) and its inverse.

These approximations, R_α,β^m,n(x) ≈ E_α,β(-x), are only valid where:

• 0 < α ≤ 1
• α ≤ β
• x ≥ 0

This is just an implementation of:

“Highly Accurate Global Pade Approximations of Generalized Mittag-Leffler Function and its Inverse” arXiv: 1912.10996

Using the library

There’s really only 2 functions you need to use:

mlp.m : Mittag-Leffler function, E_α,β(-x) imlp.m : inverse of Mittag-Leffler, -L_α,beta(y)

For how to use them, see the docs in each file.

If you want to precompute your α and β values and then more directly compute the approximant, the workflow is:

1. solvePQcoeffs.m to get polynomial coefficients of the approximant for the given α, β
2. compute4OrdPoly.m to compute the polynomial

(but note that this workflow has no error checking/input validation, so user beware)

The other files are the actual implementations of the approximants, which do no sort of input checking/sanitizing and won’t throw errors or warn you if you misuse them.