Table of Contents

The procedure **HypergeometricSolution** in the package **LFS** (Linear Functional Systems) is an implementation in Maple 2018 of an algorithm to construct a partiсular *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 particular 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

**Ai(x)**are matrices whose entries are rational functions of**x**;**b(x)**is a column vector of finite sums of hypergeometric terms of**x**;**y(x)**is a column vector of unknown functions;**ξ**is a pseudo-linear map.

The *normal form* of a first order system:

**ξ(y(x)) = A(x) y(x) + b(x)**,

where

**A(x)**is a matrix whose entries are rational functions in**x**.

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.

Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Noncommercial 3.0 Unported