A new approach to the calculation of multiloop Feynman diagrams: Gegenbauer polynomials technique in x space

The technique is described for computing dimensional regularization of Feynman integrals that is based on the use of Gegenbauer polynomials in X-space. The technique permits to analytically compute the counterterms in any theory and for any composite operators at the threeloop level in the minimum subtraction circuit. An exact calculation is presented (in all orders for epsilon=(4-D)/2) for twoloop massless diagrams of a propagator type that occur in considerations of threeloop counterterms. The technique elaborated is applied to computation of threeloop corrections to the relationship R(S)=σsub(tot)(e+e- → hadrons)/σsub(tot)(e+e- → μ+μ-) in QCD