Padé approximants

I am looking for a general package to compute Padé approximants.

In my use case these show up as part of the holomorphic load flow method (see Holomorphic Embedding Load-flow method - Wikipedia). An implementation of HELM already exists at AnalyticalLoadFlow.jl (this is just HELM under a different name), which also includes the Padé approximation as part of its implementation.

I think it would be worthwhile to setup a dedicated package for Padé approximation, as it is a quite general concept that also has clear applications in e.g. control. For my application on HELM I would then use such a package as a dependency.

If others would find this useful, have any ideas about where to host this, or have any ideas regarding implementation, please let me know!

I would be happy to host it at ComplexVariables · GitHub, if you thought that was a good fit.