I am defining a new analytic function of six variables. I have algorithms to evaluate it numerically, and have amassed a large catalog of analytic properties.
It is easy for me to program the numerics using:
funcF[a_?NumericQ, b_?NumericQ, c_?NumericQ, d_?NumericQ, e_?NumericQ, f_?NumericQ] = (*...*)
I know the analytic expression for its derivative with respect to each argument. I also know the location of all the singularities and the Taylor/asymptotic series expansion of this function near these singularities in all six variables, and a bunch of other identities.
Question: I want to make a package that incorporates this function into Mathematica. What do I need to do to to make it work as seamlessly as possible with its built-in functions like
Simplify, etc. Clearly, there will be a lot of coding to do, but I'm more than willing.
I already have a head-start from the answer to this question, which nicely makes the custom function
ln work well with
Series. I stumbled upon this page: http://functions.wolfram.com/NB/StruveH.nb which includes functions like
Singularities, etc. and thought this would be the key to accomplishing my task. Alas, these functions aren't
Mathematica functions and can't be evaluated. Is there a template/guideline for this?