Johannes Blümlein (Desy, Zeuthen)
A survey is given on the present status of analytic calculation methods and the mathematical structures of zero- and single scale Feynman amplitudes which emerge in higher order perturbative calculations in the Standard Model of elementary particles, its extensions and associated model field theories, including effective field theories of different kind. The methods include symbolic summation methods, symbolic solutions of differential equations, different classes of higher transcendental functions and special numbers. A main characteristics of the objects studied is their representation as iterative integrals, including higher transcendental letters in the associated alphabets.
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