368 research outputs found
Three Recitations on Holonomic Systems and Hypergeometric Series
A tutorial on what later became to be known as WZ theory, as well as a
motivated account of the seminal Gosper algorithm.Comment: Plain Te
Constructing minimal telescopers for rational functions in three discrete variables
We present a new algorithm for constructing minimal telescopers for rational
functions in three discrete variables. This is the first discrete
reduction-based algorithm that goes beyond the bivariate case. The termination
of the algorithm is guaranteed by a known existence criterion of telescopers.
Our approach has the important feature that it avoids the potentially costly
computation of certificates. Computational experiments are also provided so as
to illustrate the efficiency of our approach
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 difference fields, how the problems are
solved there, and how the derived results in the given difference field can be
reinterpreted as solutions of the input problem. The algorithms are illustrated
with the Mathematica package \SigmaP\ by discovering and proving new harmonic
number identities extending those from (Paule and Schneider, 2003). In
addition, the newly developed package \texttt{EvaluateMultiSums} is introduced
that combines the presented tools. In this way, large scale summation problems
for the evaluation of Feynman diagrams in QCD (Quantum ChromoDynamics) can be
solved completely automatically.Comment: Uses svmult.cls, to appear as contribution in the book "Computer
Algebra in Quantum Field Theory: Integration, Summation and Special
Functions" (www.Springer.com
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