On Rational and Hypergeometric Solutions of Linear Ordinary Difference Equations in Π^*-field extensions

by   Sergei A. Abramov, et al.

We present a complete algorithm that computes all hypergeometric solutions of homogeneous linear difference equations and rational solutions of parameterized linear difference equations in the setting of ΠΣ^*-fields. More generally, we provide a flexible framework for a big class of difference fields that is built by a tower of ΠΣ^*-field extensions over a difference field that satisfies certain algorithmic properties. As a consequence one can compute all solutions in terms of indefinite nested sums and products that arise within the components of a parameterized linear difference equation, and one can find all hypergeometric solutions that are defined over the arising sums and products of a homogeneous linear difference equation.


page 1

page 2

page 3

page 4


Solving linear difference equations with coefficients in rings with idempotent representations

We introduce a general reduction strategy that enables one to search for...

Denominator Bounds for Systems of Recurrence Equations using ΠΣ-Extensions

We consider linear systems of recurrence equations whose coefficients ar...

Summation Theory II: Characterizations of RΠΣ^*-extensions and algorithmic aspects

Recently, RΠΣ^*-extensions have been introduced which extend Karr's ΠΣ^*...

Refined telescoping algorithms in RΠΣ-extensions to reduce the degrees of the denominators

We present a general framework in the setting of difference ring extensi...

Computer Algebra and Hypergeometric Structures for Feynman Integrals

We present recent computer algebra methods that support the calculations...

Stream/block ciphers, difference equations and algebraic attacks

In this paper we model a class of stream and block ciphers as systems of...

Please sign up or login with your details

Forgot password? Click here to reset