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Starting from the Mellin-Barnes integral representation of a Feynman integraldepending on set of kinematic variables $z_i$, we derive a system of partialdifferential equations w.r.t.\ new variables $x_j$, which parameterize thedifferentiable constraints $z_i=y_i(x_j)$. In our algorithm, the powers ofpropagators can be considered as arbitrary parameters. Our algorithm can alsobe used for the reduction of multiple hypergeometric sums to sums of lowerdimension, finding special values and reduction equations of hypergeometricfunctions in a singular locus of continuous variables, or finding systems ofpartial differential equations for master integrals with arbitrary powers ofpropagators. As an illustration, we produce a differential equation of fourthorder in one variable for the one-loop two-point Feynman diagram with twodifferent masses and arbitrary propagator powers.

Specializations of partial differential equations for Feynman integrals