HypExp for Maple

HypExp can not be used directly in Maple. It is however possible to load expansions of hypergeometric functions from the libraries of HypExp. How to do that is explained in the following.

1. Install HypExp with the libraries you are intersted in.

2. copy the script MathematicaToMaple and the file MathematicaToMaple.sed in the installation directory of HypExp

3. run the script MathematicaToMaple

> sh MathematicaToMaple

This will generate a directory MapleLibs and will convert the libraries in a format readable for Maple.

4. Use the following code at the begining of your Maple Session:

first initialize the path of the maple libraries:

> installpath:="/the/hypex/installation/path/MapleLibs/":

then use the following code:

> with(StringTools):
   hypexpfilename3F2:= (a,b) -> Join(["hypexp",convert(sort(a)[1],string),convert(sort(a)[2],string),convert(sort(a)[3],string),convert(sort(b)[1],string),convert(sort(b)[2],string),".maple"],""):

  hypexpfilename2F1:= (a,b) -> Join(["hypexp",convert(sort(a)[1],string),convert(sort(a)[2],string),convert(sort(b)[1],string),".maple"],""):

  constructepsvector:= (j) -> t^(j-1):
  epsvector:= (e,j) -> subs(t=e,Vector(j,constructepsvector)):
  with(LinearAlgebra):
  sd:= (e,v,min,max) -> e^min*Multiply(Vector[row](v),epsvector(e,max-min)):

  hypexp2F1 := proc(a1,a2,b1,alpha1,alpha2,beta1,x,e)  ;
  read Join([installpath,hypexpfilename2F1([a1,a2],[b1])],"");
  hypexpresult(alpha1,alpha2,beta1,x,e);
  end proc:;

  hypexp3F2 := proc(a1,a2,a3,b1,b2,alpha1,alpha2,alpha3,beta1,beta2,x,e)  ;
  read Join([installpath,hypexpfilename3F2([a1,a2,a3],[b1,b2])],"");
  hypexpresult(alpha1,alpha2,alpha3,beta1,beta2,x,e);
  end proc:;

The expansion is then called with the function

> hypexp3F2(1,1,1,-2,2,al,a2,a3,b1,b2,z,eps);

or

> hypexp2F1(1,5,0,al,a2,b1,z,eps);

where the first 5 (3) arguments are the integer parts of the parameters of the hypergeometric function 3F2 (2F1) , the 5 (3) following arguments are the coefficients of the small parameter. The two last arguements are the variable and the small parameter in which the expansion is taken.

Expanding the libraries

If you need expansions which are not in the libraries, you should use the command HypExpAddToLib under Mathematica in order to extend the libraries, the rerun the script MathematicaToMaple. The new members of the libraries will then be accessible from Maple
Bug reports

We are not experienced Maple users, so if this does not work well or has some bugs, please tell us.