  The beta integral method proved itself as a simple nonetheless powerful
method of generating hypergeometric identities at a fixed argument. In this
paper we propose a generalization by substituting the beta density with a
particular type of Meijer's G function. By application of our method to known
transformation formulas we derive about forty hypergeometric identities,
majority of which are believed to be new. We further apply some of these
transformations to obtain several new summation formulas.
