I need to port a numerical simulation written in Wolfram Mathematica to another language. The part that is giving me trouble is that the code is calling the HermiteH function with a non-integral order (the parameter n is a fractional number, not an integer), which I'm guessing is some extension to Hermite polynomials. What algorithm can be used to implement this function and what does it actually calculate when given a non-integral order?
(I do know how to implement hermite polynomials for integral orders)
http://www.maplesoft.com/support/help/maple/view.aspx?path=HermiteH
For n different from a non-negative integer, the analytic extension of the Hermite polynomial is given by
where KummerM is a Kummer's function (of the first kind) M and Γ is a gamma function