We describe how Wegschaider's algorithm, based on WZ-summation, can be used to compute homogeneous and inhomogeneous recurrences not only for nested sums but also for multiple Mellin-Barnes integrals over hypergeometric terms.

We also include applications of this algorithmic method in the computation of Feynman parameter integrals and in the proofs of typical entries from the Gradshteyn-Ryzhik Table of Integrals.