1,830 research outputs found
A streamlined difference ring theory: Indefinite nested sums, the alternating sign and the parameterized telescoping problem
We present an algebraic framework to represent indefinite nested sums over
hypergeometric expressions in difference rings. In order to accomplish this
task, parts of Karr's difference field theory have been extended to a ring
theory in which also the alternating sign can be expressed. The underlying
machinery relies on algorithms that compute all solutions of a given
parameterized telescoping equation. As a consequence, we can solve the
telescoping and creative telescoping problem in such difference rings.Comment: Some typos are remove
Computer algebra tools for Feynman integrals and related multi-sums
In perturbative calculations, e.g., in the setting of Quantum Chromodynamics
(QCD) one aims at the evaluation of Feynman integrals. Here one is often faced
with the problem to simplify multiple nested integrals or sums to expressions
in terms of indefinite nested integrals or sums. Furthermore, one seeks for
solutions of coupled systems of linear differential equations, that can be
represented in terms of indefinite nested sums (or integrals). In this article
we elaborate the main tools and the corresponding packages, that we have
developed and intensively used within the last 10 years in the course of our
QCD-calculations
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
single scale quantities using the systems of differential and/or difference
equations obtained by integration-by-parts identities between the corresponding
Feynman integrals of loop corrections to physical quantities. These scalar
quantities have a much simpler mathematical structure than the complete
quantity. A sufficiently large set of moments may even allow the analytic
reconstruction of the whole quantity considered, holding in case of first order
factorizing systems. In any case, one may derive highly precise numerical
representations in general using this method, which is otherwise completely
analytic.Comment: 4 pages LATE
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