
Solving linear difference equations with coefficients in rings with idempotent representations
We introduce a general reduction strategy that enables one to search for...
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Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation
A general overview of the existing difference ring theory for symbolic s...
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Representation of hypergeometric products of higher nesting depths in difference rings
A nontrivial symbolic machinery is presented that can rephrase algorith...
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On Rational and Hypergeometric Solutions of Linear Ordinary Difference Equations in Π^*field extensions
We present a complete algorithm that computes all hypergeometric solutio...
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A case study for ζ(4)
Using symbolic summation tools in the setting of difference rings, we pr...
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The AbsentMinded Passengers Problem: A Motivating Challenge Solved by Computer Algebra
In (S.B. Ekhad and D. Zeilberger, 2020) an exciting case study has been ...
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A refined machinery to calculate large moments from coupled systems of linear differential equations
The large moment method can be used to compute a large number of moments...
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Minimal representations and algebraic relations for single nested products
Recently, it has been shown constructively how a finite set of hypergeom...
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Towards a symbolic summation theory for unspecified sequences
The article addresses the problem whether indefinite double sums involvi...
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Computer algebra tools for Feynman integrals and related multisums
In perturbative calculations, e.g., in the setting of Quantum Chromodyna...
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Refined Holonomic Summation Algorithms in Particle Physics
An improved multisummation approach is introduced and discussed that en...
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Representing (q)hypergeometric products and mixed versions in difference rings
In recent years, Karr's difference field theory has been extended to the...
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Denominator Bounds for Systems of Recurrence Equations using ΠΣExtensions
We consider linear systems of recurrence equations whose coefficients ar...
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The Method of Arbitrarily Large Moments to Calculate Single Scale Processes in Quantum Field Theory
We device a new method to calculate a large number of Mellin moments of ...
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Algorithms to solve coupled systems of differential equations in terms of power series
Using integration by parts relations, Feynman integrals can be represent...
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Evaluation of binomial double sums involving absolute values
We show that double sums of the form ∑_i,j=n ^n i^sj^t(i^kj^k)^β 2n...
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Asymptotic and exact results on the complexity of the NovelliPakStoyanovskii algorithm
The NovelliPakStoyanovskii algorithm is a sorting algorithm for Young ...
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Summation Theory II: Characterizations of RΠΣ^*extensions and algorithmic aspects
Recently, RΠΣ^*extensions have been introduced which extend Karr's ΠΣ^*...
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A toolbox to solve coupled systems of differential and difference equations
We present algorithms to solve coupled systems of linear differential eq...
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Algebraic independence of sequences generated by (cyclotomic) harmonic sums
An expression in terms of (cyclotomic) harmonic sums can be simplified b...
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Carsten Schneider
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