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HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: and Horn-type hypergeometric functions of three variables
Vladimir V. Bytev, Mikhail Yu. Kalmykov, Sven-Olaf Moch
HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two p…
Feynman integrals and difference equations
S. Moch, C. Schneider
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations…
Symbolic Summation and Higher Orders in Perturbation Theory
S. Moch
Higher orders in perturbation theory require the calculation of Feynman integrals at multiple loops. We report on an approach to systematically solve Feynman integrals by means of…
- XSummer - Transcendental Functions and Symbolic Summation in Form
S. Moch, P. Uwer
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been th…