Incomplete Gamma with Complex input

question

#1

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


#2

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.


#3

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


#4

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.


#5

There’s also HypergeometricFunctions inside SingularIntegralEquations.jl. We’re in the process of splitting it out: https://github.com/JuliaApproximation/HypergeometricFunctions.jl


#6

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

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.