Thoughts of new algorithms?

[putianyi889]

This matlab code is related to a paper from 2015.
https://au.mathworks.com/matlabcentral/fileexchange/48154-the-mittag-leffler-function

I've translated the codes into Julia. I'm daily using this algorithm without testing many cases. It computes correctly so far and is much faster than this Julia package. I'm wondering if the package can move to the new algorithm.

[jlapeyre]

Sorry I just saw this now. Yes, this is potentially very interesting!
If it is correct and fast that would be great. I don't have Mathematica installed right now. But I could do it. It would be good to compare whatever tests we do to Mma. It is not foolproof. But, there is not much else out there.