Differential equations and high-energy expansion of two-loop diagrams in D dimensions

New method of calculation of master integrals using differential equations and asymptotical expansion is presented. This method leads to the results exact in space–time dimension D   having the form of the convergent power series. As an application of this method, we calculate the two-loop master integral for “crossed-triangle” topology which was previously known only up to O(ε)O(ε) order. The case when a topology contains several master integrals is also considered. We present an algorithm of the term-by-term calculation of the asymptotical expansion in this case and analyze in detail the “crossed-box” topology with three master integrals.