Differential Reduction Algorithms for Hypergeometric Functions Applied to Feynman Diagram Calculation

with the arguments xj being, in general, rational functions (typically, simple ratios) of kinematic invariants of the original Feynman diagram, and the parameters {γj} and {σk} being linear combinations of the exponents of propagators and the dimension of space-time. The γj and σk are called upper and lower parameters, respectively. These statements follow from the multiple Mellin-Barnes representation for a dimensionally regularized Feynman diagram (see Ref. [4]), and the assumption that there is a region of variables where every term in the linear combination (1) is convergent. The Horn-type structure permits the hypergeometric functions appearing in (1) to be reduced to a set of