Iterated integrals over letters induced by quadratic forms
Jakob Ablinger, J. Blümlein, Carsten Schneider
Abstract
An automated treatment of iterated integrals based on letters induced by real-valued quadratic forms and Kummer--Poincar\'e letters is presented. These quantities emerge in analytic single and multiscale Feynman diagram calculations. To compactify representations, one wishes to apply general properties of these quantities in computer-algebraic implementations. We provide the reduction to basis representations, expansions, analytic continuation and numerical evaluation of these quantities.
Topics & Concepts
Iterated functionQuadratic equationFeynman diagramAnalytic continuationContinuationAlgebraic numberMathematicsAlgebra over a fieldApplied mathematicsBasis (linear algebra)Reduction (mathematics)Meromorphic functionRegularization (linguistics)Pure mathematicsComputer scienceMathematical analysisMathematical physicsArtificial intelligenceGeometryProgramming languageAdvanced Mathematical IdentitiesAlgebraic structures and combinatorial modelsPolynomial and algebraic computation