Carsten Schneider

J. Symb. Comput., 2025

2024

Representation of hypergeometric products of higher nesting depths in difference rings.

[BibT_eX]

[DOI]

Evans Doe Ocansey

J. Symb. Comput., 2024

Challenges for analytic calculations of the massive three-loop form factors.

[BibT_eX]

[DOI]

CoRR, 2024

2023

Hypergeometric structures in Feynman integrals.

[BibT_eX]

[DOI]

Marco Saragnese

Ann. Math. Artif. Intell., October, 2023

Computing Mellin Representations and Asymptotics of Nested Binomial Sums in a Symbolic Way: The RICA Package.

[BibT_eX]

[DOI]

Nikolai Fadeev

ACM Commun. Comput. Algebra, June, 2023

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

[BibT_eX]

[DOI]

Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation, 2023

2022

Error bounds for the asymptotic expansion of the partition function.

[BibT_eX]

[DOI]

CoRR, 2022

Computer Algebra and Hypergeometric Structures for Feynman Integrals.

[BibT_eX]

[DOI]

Marco Saragnese

CoRR, 2022

The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals.

[BibT_eX]

[DOI]

CoRR, 2022

2021

The Absent-Minded Passengers Problem: A Motivating Challenge Solved by Computer Algebra.

[BibT_eX]

[DOI]

Math. Comput. Sci., 2021

On rational and hypergeometric solutions of linear ordinary difference equations in ΠΣ⁎-field extensions.

[BibT_eX]

[DOI]

J. Symb. Comput., 2021

Iterated integrals over letters induced by quadratic forms.

[BibT_eX]

[DOI]

CoRR, 2021

Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation.

[BibT_eX]

[DOI]

CoRR, 2021

Solving Linear Difference Equations with Coefficients in Rings with Idempotent Representations.

[BibT_eX]

[DOI]

Proceedings of the ISSAC '21: International Symposium on Symbolic and Algebraic Computation, 2021

2020

Minimal Representations and Algebraic Relations for Single Nested Products.

[BibT_eX]

[DOI]

Program. Comput. Softw., 2020

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

[BibT_eX]

[DOI]

CoRR, 2020

A case study for ζ(4).

[BibT_eX]

[DOI]

Wadim Zudilin

CoRR, 2020

2019

Numerical implementation of harmonic polylogarithms to weight w = 8.

[BibT_eX]

[DOI]

Comput. Phys. Commun., 2019

A refined machinery to calculate large moments from coupled systems of linear differential equations.

[BibT_eX]

[DOI]

Peter Marquard

CoRR, 2019

2018

Towards a symbolic summation theory for unspecified sequences.

[BibT_eX]

[DOI]

CoRR, 2018

Computer algebra tools for Feynman integrals and related multi-sums.

[BibT_eX]

[DOI]

CoRR, 2018

Towards a direct method for finding hypergeometric solutions of linear first order recurrence systems.

[BibT_eX]

[DOI]

Johannes Middeke

ACM Commun. Comput. Algebra, 2018

2017

Summation Theory II: Characterizations of RΠΣ⁎-extensions and algorithmic aspects.

[BibT_eX]

[DOI]

J. Symb. Comput., 2017

Representing ($q$-)hypergeometric products and mixed versions in difference rings.

[BibT_eX]

[DOI]

Evans Doe Ocansey

CoRR, 2017

Denominator Bounds for Systems of Recurrence Equations using $ΠΣ$-Extensions.

[BibT_eX]

[DOI]

Johannes Middeke

CoRR, 2017

The Method of Arbitrarily Large Moments to Calculate Single Scale Processes in Quantum Field Theory.

[BibT_eX]

[DOI]

CoRR, 2017

Refined Holonomic Summation Algorithms in Particle Physics.

[BibT_eX]

[DOI]

Mark Round

CoRR, 2017

Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams.

[BibT_eX]

[DOI]

CoRR, 2017

Asymptotic and Exact Results on the Complexity of the Novelli-Pak-Stoyanovskii Algorithm.

[BibT_eX]

[DOI]

Robin Sulzgruber

Electron. J. Comb., 2017

2016

A difference ring theory for symbolic summation.

[BibT_eX]

[DOI]

J. Symb. Comput., 2016

Calculating three loop ladder and V-topologies for massive operator matrix elements by computer algebra.

[BibT_eX]

[DOI]

Andreas von Manteuffel

Comput. Phys. Commun., 2016

Evaluation of binomial double sums involving absolute values.

[BibT_eX]

[DOI]

Christian Krattenthaler

CoRR, 2016

A toolbox to solve coupled systems of differential and difference equations.

[BibT_eX]

[DOI]

CoRR, 2016

Algorithms to solve coupled systems of differential equations in terms of power series.

[BibT_eX]

[DOI]

CoRR, 2016

Representation of hypergeometric products in difference rings.

[BibT_eX]

[DOI]

Evans Doe Ocansey

ACM Commun. Comput. Algebra, 2016

Denominator bounds for higher order systems of linear recurrence equations.

[BibT_eX]

[DOI]

Johannes Middeke

ACM Commun. Comput. Algebra, 2016

Symbolic Summation in Difference Rings and Applications.

[BibT_eX]

[DOI]

Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, 2016

2015

Fast Algorithms for Refined Parameterized Telescoping in Difference Fields.

[BibT_eX]

[DOI]

Proceedings of the Computer Algebra and Polynomials, 2015

Algebraic independence of (cyclotomic) harmonic sums.

[BibT_eX]

[DOI]

CoRR, 2015

2014

Recent Symbolic Summation Methods to Solve Coupled Systems of Differential and Difference Equations.

[BibT_eX]

[DOI]

Abilio De Freitas

CoRR, 2014

Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams.

[BibT_eX]

[DOI]

CoRR, 2014

A Streamlined Difference Ring Theory: Indefinite Nested Sums, the Alternating Sign, and the Parameterized Telescoping Problem.

[BibT_eX]

[DOI]

Proceedings of the 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 2014

2013

Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order

[BibT_eX]

[DOI]

CoRR, 2013

Simplifying Multiple Sums in Difference Fields

[BibT_eX]

[DOI]

CoRR, 2013

Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms

[BibT_eX]

[DOI]

CoRR, 2013

Modern Summation Methods for Loop Integrals in Quantum Field Theory: The Packages Sigma, EvaluateMultiSums and SumProduction.

[BibT_eX]

[DOI]

CoRR, 2013

Fast Algorithms for Refined Parameterized Telescoping in Difference Fields.

[BibT_eX]

[DOI]

CoRR, 2013

2012

A symbolic summation approach to Feynman integral calculus.

[BibT_eX]

[DOI]

J. Symb. Comput., 2012

Advanced Computer Algebra Algorithms for the Expansion of Feynman Integrals

[BibT_eX]

[DOI]

CoRR, 2012

Evaluation of Multi-Sums for Large Scale Problems.

[BibT_eX]

[DOI]

Alexander Hasselhuhn

CoRR, 2012

2011

Unfair permutations.

[BibT_eX]

[DOI]

Helmut Prodinger

Stephan G. Wagner

Eur. J. Comb., 2011

Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials

[BibT_eX]

[DOI]

CoRR, 2011

A refined denominator bounding algorithm for multivariate linear difference equations.

[BibT_eX]

[DOI]

Proceedings of the Symbolic and Algebraic Computation, International Symposium, 2011

2010

A symbolic summation approach to feynman integrals.

[BibT_eX]

[DOI]

ACM Commun. Comput. Algebra, 2010

Structural theorems for symbolic summation.

[BibT_eX]

[DOI]

Appl. Algebra Eng. Commun. Comput., 2010

Towards an Eclipse Ontology Framework: Integrating OWL and the Eclipse Modeling Framework.

[BibT_eX]

[DOI]

Proceedings of the 3rd Workshop on Transforming and Weaving Ontologies in Model Driven Engineering, 2010

Partial denominator bounds for partial linear difference equations.

[BibT_eX]

[DOI]

Proceedings of the Symbolic and Algebraic Computation, International Symposium, 2010

2009

Gaussian Hypergeometric series and supercongruences.

[BibT_eX]

[DOI]

Robert Osburn

Math. Comput., 2009

Determining the closed forms of the O(sS3) anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra.

[BibT_eX]

[DOI]

Comput. Phys. Commun., 2009

A Symbolic Summation Approach to Find Optimal Nested Sum Representations

[BibT_eX]

[DOI]

CoRR, 2009

From Moments to Functions in Quantum Chromodynamics

[BibT_eX]

[DOI]

CoRR, 2009

Determining the closed forms of the $O(a_s^3)$ anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra

[BibT_eX]

[DOI]

CoRR, 2009

Algorithms in Symbolic Computation.

[BibT_eX]

[DOI]

Proceedings of the Hagenberg Research, 2009

2008

A refined difference field theory for symbolic summation.

[BibT_eX]

[DOI]

J. Symb. Comput., 2008

Parameterized Telescoping Proves Algebraic Independence of Sums

[BibT_eX]

[DOI]

CoRR, 2008

Automated Proofs for Some Stirling Number Identities.

[BibT_eX]

[DOI]

Electron. J. Comb., 2008

Multi-summation in difference fields (abstract only).

[BibT_eX]

[DOI]

ACM Commun. Comput. Algebra, 2008

2007

When Is 0.999... Equal to 1?

[BibT_eX]

[DOI]

Robin Pemantle

Am. Math. Mon., 2007

Difference Equations in Massive Higher Order Calculations

[BibT_eX]

[DOI]

CoRR, 2007

Apery's Double Sum is Plain Sailing Indeed.

[BibT_eX]

[DOI]

Electron. J. Comb., 2007

Symbolic summation with radical expressions.

[BibT_eX]

[DOI]

Proceedings of the Symbolic and Algebraic Computation, International Symposium, 2007

2006

Indefinite summation with unspecified summands.

[BibT_eX]

[DOI]

Discret. Math., 2006

Hypergeometric Summation Algorithms for High-order Finite Elements.

[BibT_eX]

[DOI]

Computing, 2006

Application of unspecified sequences in symbolic summation.

[BibT_eX]

[DOI]

Proceedings of the Symbolic and Algebraic Computation, International Symposium, 2006

Factor Analysis for Extraction of Structural Components and Prediction in Time Series.

[BibT_eX]

[DOI]

Gerhard Arminger

Proceedings of the Advances in Data Analysis, 2006

2005

A new Sigma approach to multi-summation.

[BibT_eX]

[DOI]

Adv. Appl. Math., 2005

Plane partitions VI: Stembridge's TSPP theorem.

[BibT_eX]

[DOI]

George E. Andrews

Adv. Appl. Math., 2005

Degree Bounds to Find Polynomial Solutions of Parameterized Linear Difference Equations in Pi-Sigma-Fields.

[BibT_eX]

[DOI]

Appl. Algebra Eng. Commun. Comput., 2005

Finding telescopers with minimal depth for indefinite nested sum and product expressions.

[BibT_eX]

[DOI]

Proceedings of the Symbolic and Algebraic Computation, 2005

Some Notes On "When is 0.999... equal to 1?".

[BibT_eX]

[DOI]

Proceedings of the Mathematics, Algorithms, Proofs, 9.-14. January 2005, 2005

2004

The Summation Package Sigma: Underlying Principles and a Rhombus Tiling Application.

[BibT_eX]

[DOI]

Discret. Math. Theor. Comput. Sci., 2004

Symbolic summation with single-nested sum extensions.

[BibT_eX]

[DOI]

Proceedings of the Symbolic and Algebraic Computation, 2004

2003

Computer proofs of a new family of harmonic number identities.

[BibT_eX]

[DOI]