Weixlbaumer C. Solutions Of Difference Equations With Polynomial Coefficients

Linz: Jogannes Kepler Universitat, 2001. — 129 p.A Historical SurveyNotations and Basic Definitions
Basics
Sequences, Functions, and Operators
The Falling and Rising Factorial and the GFF
Hypergeometric Terms
Difference Equations
Basic Theory About Difference Operators
Solutions of Difference Equations
Operations on Difference Operators
The Adjoint Operator
The Symmetric Product
The Greatest Common Right Divisor
The Lowest Common Left Multiple
Polynomial Solutions
The Basic Idea
Abramov and the Delta-Operator
Petkovsek and the Shift-Operator
Minimizing The Number Of Variables
Solving by Interpolation Techniques
Using Lagrange Interpolation
Using Newton Interpolation
Comparing the Bounds
Examples and Comparison
Rational Solutions
The Universal Denominator By Abramov
The Denominator Bound By van Hoeij
Improving The Scalar Case
Examples and Comparison
Hypergeometric Solutions
Petkovsek's Hyper
Van Hoeij's Singularities-Approach
Computing valuation growths
Examples and Comparison
Inhomogeneous Equations
Gosper's Algorithm
Generalizations of Gosper's Algorithm
Increasing the Order by $
Examples
D'Alembertian Solutions
The Reduction Of Order
Inhomogeneous Equations
A Slight Improvement
Examples