The SAGEX review on scattering amplitudes Chapter 4: Multi-loop Feynman integrals

J Blümlein, C Schneider - Journal of Physics A: Mathematical and …, 2022‏ - iopscience.iop.org
The analytic integration and simplification of multi-loop Feynman integrals to special
functions and constants plays an important role to perform higher order perturbative …

Simplifying multiple sums in difference fields

C Schneider - Computer Algebra in Quantum Field Theory …, 2013‏ - Springer
In this survey article we present difference field algorithms for symbolic summation. Special
emphasize is put on new aspects in how the summation problems are rephrased in terms of …

Hypergeometric summation

W Koepf - Vieweg, Braunschweig/Wiesbaden, 1998‏ - Springer
The first edition of this book appeared in 1998 and was published by Vieweg
(Braunschweig/Wiesbaden). Several years later, the book was sold out and no longer …

[PDF][PDF] Symbolic summation assists combinatorics

C Schneider - Sém. Lothar. Combin, 2007‏ - gwdg.de
Part 1. Symbolic summation methods and applications Page 1 Séminaire Lotharingien de
Combinatoire 56 (2007), Article B56b SYMBOLIC SUMMATION ASSISTS COMBINATORICS …

[كتاب][B] Polynomial algorithms in computer algebra

F Winkler - 1996‏ - books.google.com
For several years now I have been teaching courses in computer algebra at the Universitat
Linz, the University of Delaware, and the Universidad de Alcala de Henares. In the summers …

The concrete tetrahedron

M Kauers - Proceedings of the 36th international symposium on …, 2011‏ - dl.acm.org
The concrete tetrahedron Page 1 The Concrete Tetrahedron Manuel Kauers ∗ RISC Johannes
Kepler University 4040 Linz (Austria) mkauers@risc.jku.at ABSTRACT We give an overview …

A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities

P Paule, M Schorn - Journal of symbolic computation, 1995‏ - Elsevier
Based on Gosper's algorithm for indefinite hypergeometric summation, Zeilberger's
algorithm for proving binomial coefficient identities constitutes a recent breakthrough in …

[PDF][PDF] A Mathematica q-analogue of Zeilberger's algorithm based on an algebraically motivated approach to q-hypergeometric telesco**

P Paule, A Riese - Special functions, q-series and related topics, 1997‏ - risc.jku.at
Mathematica implementations, available by email request, of q-analogues of Gosper's and
Zeilberger's algorithm are described. Nontrivial examples are given in order to illustrate the …

[كتاب][B] Symbolic summation in difference fields

C Schneider - 2001‏ - risc.jku.at
There are implementations of the celebrated Gosper algorithm (1978) on almost any
computer algebra platform. Within my PhD thesis work I implemented Karr's Summation …

Differential Galois theory of linear difference equations

C Hardouin, MF Singer - Mathematische Annalen, 2008‏ - Springer
We present a Galois theory of difference equations designed to measure the differential
dependencies among solutions of linear difference equations. With this we are able to …