Appel F1 implementation in Julia?

LolianSh · March 6, 2023, 2:52am

Hi, do you guys know if there is any impelemntation of the Appel hypergeometric function in Julia?

AppellF1[a, b1, b2, c, x, y]

I had a look into HypergeometricFunctions.jl, but only found the implementation of Gauss’s hypergeometric series.

jd-foster · March 6, 2023, 3:35am

This has an open issue with some nice advice from @TSGut here

github.com/JuliaMath/HypergeometricFunctions.jl

Add Appell functions?

opened 11:37PM - 05 Nov 20 UTC

TSGut

Any interest or obvious route from the current implementations to adding [Appell… function](https://dlmf.nist.gov/16.13) support to this package? I would mainly be interested in F1 for my application case. It seems currently the only reasonable implementations of these functions are in the form of [this Fortran package](https://data.mendeley.com/datasets/9tvmt9d8yj/1), which also has [an R wrapper](https://www.rdocumentation.org/packages/appell/versions/0.0-4/topics/appellf1), and the as far as I can tell independent implementation in [the Python package mpmath](https://github.com/fredrik-johansson/mpmath) - see also the [documentation on mpmath](http://mpmath.org/doc/current/functions/hypergeometric.html). Would be nice to be able to do this in Julia as well. Writing a wrapper would be straightforward but perhaps not in the spirit of the package?