Alan,So, given these functions should be available in Fortran, perhaps I should try this:Yeah, typically a Fortran era function that has not (yet) been ported to C++.Re a C/C++ version, I thought a little about that several days ago. The main bottleneck there is I need two special functions with all complex arguments: the Bessel I(nu,z) and the confluent hypergeometric M(a,b,z). Googling, I could only locate one library supporting those and it was not really set up for Windows, my current environment. If anybody knows such a library that can easily be hooked in to Visual Studio on Windows, I'd appreciate a link. (Some usual suspects, Boost and GSL, don't have the complex argument support, as far as I could tell).

https://en.wikipedia.org/wiki/Intel_Fortran_Compiler

I am looking for option pricing (numerical) data to test [$]M(a,b,z)[$] against option prices for [$]a,b \in \mathbb R, z \in \mathbb C [$].

Your section 1.6 seems to be related to this question.