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08/11/2023
Computing Mellin representations and asymptotics of nested binomial sums in a symbolic way: the RICA package
Nested binomial sums form a particular class of sums that arise in the c...
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02/07/2023
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...
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09/16/2022
Error bounds for the asymptotic expansion of the partition function
Asymptotic study on the partition function p(n) began with the work of H...
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07/18/2022
Computer Algebra and Hypergeometric Structures for Feynman Integrals
We present recent computer algebra methods that support the calculations...
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03/24/2022
The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
The analytic integration and simplification of multi-loop Feynman integr...
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02/05/2021
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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02/02/2021
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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11/17/2020
Representation of hypergeometric products of higher nesting depths in difference rings
A non-trivial symbolic machinery is presented that can rephrase algorith...
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05/11/2020
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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04/17/2020
A case study for ζ(4)
Using symbolic summation tools in the setting of difference rings, we pr...
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03/04/2020
The Absent-Minded 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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12/09/2019
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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11/12/2019
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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09/18/2018
Towards a symbolic summation theory for unspecified sequences
The article addresses the problem whether indefinite double sums involvi...
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09/17/2018
Computer algebra tools for Feynman integrals and related multi-sums
In perturbative calculations, e.g., in the setting of Quantum Chromodyna...
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06/12/2017
Refined Holonomic Summation Algorithms in Particle Physics
An improved multi-summation approach is introduced and discussed that en...
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05/03/2017
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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04/30/2017
Denominator Bounds for Systems of Recurrence Equations using ΠΣ-Extensions
We consider linear systems of recurrence equations whose coefficients ar...
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01/17/2017
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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08/18/2016
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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07/18/2016
Evaluation of binomial double sums involving absolute values
We show that double sums of the form ∑_i,j=-n ^n |i^sj^t(i^k-j^k)^β| 2n...
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06/24/2016
Asymptotic and exact results on the complexity of the Novelli-Pak-Stoyanovskii algorithm
The Novelli-Pak-Stoyanovskii algorithm is a sorting algorithm for Young ...
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03/14/2016
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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01/08/2016
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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10/13/2015