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Feynman Graphs
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In these lectures I discuss Feynman graphs and the associated Feynman integrals. Of particular interest are the classes functions, which appear in the evaluation of Feynman integrals. The most prominent class of functions is given by multiple polylogarithms. The algebraic properties of multiple polylogarithms are reviewed in the second part of these lectures. The final part of these lectures is devoted to Feynman integrals, which cannot be expressed in terms of multiple polylogarithms. Methods from algebraic geometry provide tools to tackle these integrals.
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Feynman Fox integrals in the physical region
A recipe is given that expresses physical-region Feynman integrals as Fox functions on vertical Mellin-Barnes contours with the correct cut structure, but the claimed imaginary-part correctness is not yet verified.
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