A symbolic summation approach to Feynman integral calculus

We discuss two methods based on Wilf-Zeilberger summation for the computation of Feynman parameter integrals. For the first method, the integrals are rewritten as multisums of hypergeometric terms to fit the input class of WZ-summation. These summation problems are highly nested sums with non-standard boundary conditions. They satisfy inhomogeneous recurrences containing sums of lower nested depth on the right-hand sides. These last recurrences can be solved recursively by Carsten Schneider’s Sigma package. Another approach to evaluate Feynman integrals is by representing them as nested Mellin-Barnes integrals. We show how WZ-methods determine recurrences for contour integrals of this type, thus eliminating the need to find sum representations. This algorithmic technique is also applied to prove typical entries from the Gradshteyn-Ryzhik table of integrals using the Mellin transform method. This work is part of my PhD thesis, defended this year at RISC, Johannes Kepler University Linz, Austria.