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: appell4 : Macros in libraries : annfs


param appell1 c
array param; array c;
appell1 returns an annihilating ideal for 
the Lauricella function F_D(a,b_1, ..., b_n,c; x_1,...,x_n)
for the parameter << param >> = [a, c, b_1, ..., b_n].
In case of n=2, the function is called the Appell function F_1.
c = [ generators,  variables ]
Note that for a special set of parameters, the returned differential equation
is not holonomic, e.g., [[1 2 3 4]] appell1 rank ::
This happens because we do not included the Euler-Darboux operators
in the return value of appell1. It will be included in a future.
Example: [ [1 -4 -2 5 6] ] appell1 rank ::
For details, see P.Appell et Kampe de Feriet, Fonction hypergeometrique
et hyperspheriques -- polynomes d'Hermite, Gauthier-Villars, 1926.

Nobuki Takayama 平成22年2月8日