The inverse Mellin transform via analytic continuation

A bstract We present a method to calculate the x -space expressions of massless or massive operator matrix elements in QCD and QED containing local composite insertions, depending on discrete Mellin index N , directly, without computing Mellin-space explicit form analytically. Here belongs either even odd positive integers. The is based resummation operators into effective propagators relies an analytic continuation between two continuous variables. apply it iterated integrals as well more general case non-iterative integrals, generalizing former ones. are needed derive small- behaviour respective quantities, which usually cannot be accessed -space. illustrate for different (iterated) alphabets, including 2 F 1 elliptic structures, examples. These structures occur three-loop calculations. Likewise applies closed solutions cases differential equations do not factorize first-order factors.