Numerical calculation of H function?

This is really rather out of the scope of Yahoo Answers. It's unreasonable to expect a forum such as this to be able to help you with mathematics much past the undergraduate level. Anything with a contour integral in it is pretty much ruled out a priori. In the Mathworld site it says, "A. Kilbas has derived a complete description for the asymptotic expansion of the -function." I'd try looking there.