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NDIM (Negative Dimensional Integration Method) is a technique for evaluatingFeynman integrals based on the concept of analytic continuation. The method hasbeen successfully applied to many diagrams in covariant and noncovariant gaugefield interactions and has shown its utility as a powerful technique to handleFeynman loop integrations in quantum field theories. In principle NDIM canhandle any loop calculation; however, in practical terms, the resultingmultiseries with several variables in general cannot be summed up convenientlyand its analytic properties are generally unknown.  The alternative then is to use order by order (loop by loop) integration inwhich the first integral is of the triangle diagram type. However, thena\"{i}ve momentum integration of this leads to wrong results. Here we use theshortened version for the triangle in NDIM that is suitable for a loop by loopcalculation and show that it leads (after appropriate analytic continuation topositive dimension) to agreement with the known result for the two-loop masterdiagram. From it, a three-loop is then calculated and shown again itsconsistency with the already published result for such a diagram.

Massless two-loop "master" and three-loop two point function in NDIM