225 citations · 3.5k across the 94 of their papers we have counts for
30 papers · 1 filter
Creative Telescoping for Hypergeometric Double Sums
Peter Paule, Carsten Schneider
We present efficient methods for calculating linear recurrences of hypergeometric double sums and, more generally, of multiple sums. In particular, we supplement this approach with…
Refined telescoping algorithms in -extensions to reduce the degrees of the denominators
Carsten Schneider
We present a general framework in the setting of difference ring extensions that enables one to find improved representations of indefinite nested sums such that the arising denomi…
Solving linear difference equations with coefficients in rings with idempotent representations
Jakob Ablinger, Carsten Schneider
We introduce a general reduction strategy that enables one to search for solutions of parameterized linear difference equations in difference rings. Here we assume that the ring it…
Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation
Carsten Schneider
A general overview of the existing difference ring theory for symbolic summation is given. Special emphasis is put on the user interface: the translation and back translation of th…
Representation of hypergeometric products of higher nesting depths in difference rings
Evans Doe Ocansey, Carsten Schneider
A non-trivial symbolic machinery is presented that can rephrase algorithmically a finite set of nested hypergeometric products in appropriately designed difference rings. As a cons…
On Rational and Hypergeometric Solutions of Linear Ordinary Difference Equations in -field extensions
Sergei A. Abramov, Manuel Bronstein, Marko Petkovšek +1
We present a complete algorithm that computes all hypergeometric solutions of homogeneous linear difference equations and rational solutions of parameterized linear difference equa…