The SAGEX review on scattering amplitudes Chapter 4: Multi-loop Feynman integrals
The analytic integration and simplification of multi-loop Feynman integrals to special
functions and constants plays an important role to perform higher order perturbative …
functions and constants plays an important role to perform higher order perturbative …
Simplifying multiple sums in difference fields
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 …
emphasize is put on new aspects in how the summation problems are rephrased in terms of …
Hypergeometric summation
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 …
(Braunschweig/Wiesbaden). Several years later, the book was sold out and no longer …
[PDF][PDF] Symbolic summation assists combinatorics
Part 1. Symbolic summation methods and applications Page 1 Séminaire Lotharingien de
Combinatoire 56 (2007), Article B56b SYMBOLIC SUMMATION ASSISTS COMBINATORICS …
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 …
Linz, the University of Delaware, and the Universidad de Alcala de Henares. In the summers …
The concrete tetrahedron
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 …
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
Based on Gosper's algorithm for indefinite hypergeometric summation, Zeilberger's
algorithm for proving binomial coefficient identities constitutes a recent breakthrough in …
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**
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 …
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 …
computer algebra platform. Within my PhD thesis work I implemented Karr's Summation …
Differential Galois theory of linear difference equations
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 …
dependencies among solutions of linear difference equations. With this we are able to …