Meromorphic solutions of recurrence relations and DRA method for multicomponent master integrals

We formulate a method to find the meromorphic solutions of higher-order recurrence relations in the form of the sum over poles with coefficients defined recursively. Several explicit examples of the application of this technique are given. The main advantage of the described approach is that the analytical properties of the solutions are very clear (the position of poles is explicit, the behavior at infinity can be easily determined). These are exactly the properties that are required for the application of the multiloop calculation method based on dimensional recurrence relations and analyticity (the DRA method).Comment: 20 pages, minor change

Total Born cross section of e+e−e^+e^--pair production in relativistic ion collisions from differential equations

We apply the differential equation method to the calculation of the total Born cross section of the process $Z_1Z_2\to Z_1Z_2e^+e^-$. We obtain explicit expression for the cross section exact in the relative velocity of the nuclei.Comment: 5 pages, 2 figures, ancillary file MastersExpansion.m attached to submissio