Iterated integrals over letters induced by quadratic forms

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 multi–scale 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.