Specializations of partial differential equations for Feynman integrals

Starting from the Mellin–Barnes integral representation of a Feynman depending on set kinematic variables zi, we derive system partial differential equations w.r.t. new xj, which parameterize differentiable constraints zi=yi(xj). In our algorithm, powers propagators can be considered as arbitrary parameters. Our algorithm also used for reduction multiple hypergeometric sums to lower dimension, finding special values and functions in singular locus continuous variables, or systems master integrals with propagators. As an illustration, produce equation fourth order one variable one-loop two-point diagram two different masses propagator powers.