Does julia 1.0 have any implementation of incomplete gamma that takes complex values? The GSL version takes reals only.

The incomplete gamma may be expressed (in several ways) in terms of the hypergeometric function {}_1F_1, which may be expressed as a limit of {}_2F_1.

GSL seems to have an implementation of {}_2F_1 with some of the arguments complex, so depending on which variable you want to take complex values, it might be useful.

Thanks for the info, that is useful to keep in mind. It is the parameter that is complex, not the integration bound.

Check Nemo: http://nemocas.github.io/Nemo.jl/latest/acb.html#Nemo.gamma-Tuple{acb,acb}

I’ve only used it with real values, but it accepts complex values too.

There’s also HypergeometricFunctions inside SingularIntegralEquations.jl. We’re in the process of splitting it out: GitHub - JuliaMath/HypergeometricFunctions.jl: A Julia package for calculating hypergeometric functions

Also this here, but it’s not up to date

https://github.com/jkovacic/IncGammaBeta.jl

I think it would be a fun exercise to write up my own Hypergeometric package too.

The GSL hypergeometric functions do not suit my needs.