This is an old revision of the document!


Hypergeometric solutions for linear functional systems

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.

A system can be represented in several forms.

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.

Source

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.

lfs.1534064657.txt.gz · Last modified: 2018/08/12 12:04 by anna
 
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Noncommercial 3.0 Unported
Recent changes RSS feed Donate Powered by PHP Valid XHTML 1.0 Valid CSS Driven by DokuWiki