This is an old revision of the document!
The procedure HypergeometricSolution in the package LFS (Linear Functional Systems) is an implementation in Maple 2018 of an algorithm to construct a partial hypergeometric solutions for inhomogeneous systems of linear differential, difference and q-difference equations with rational-function coefficients and hypergeometric right-hand sides.
Additionally, a procedure RationalSolution construct a partial rational solutions for systems with rational-function coefficients and rational-function right-hand sides.
The matrix form of a full-rank system:
An(x) ξ^n(y(x)) + … + A1(x) ξ(y(x)) + A0(x) y(x) = b(x),
where
The normal form of a first order system:
ξ(y(x)) = A(x) y(x) + b(x),
where
For the differential case: ξ(y(x)) = y'(x).
For the difference case: ξ(y(x)) = y(x+1).
For the q-difference case: ξ(y(x)) = y(q x), where q is a name or an integer large then 1.
lfs.mpl - the Maple code of the package (implemented by A.A.Ryabenko, D.E.Khmelnov).
lfs_examples.mw - the Maple session file with examples.
lfs_examples.pdf - the pdf copy of that Maple session.