Algorithm to find an all-order in the running coupling solution to an equation of the DGLAP type

Abstract

We propose an algorithm to find a solution to an integro-differential equation of the DGLAP type for all the orders in the running coupling $\alpha$ with splitting functions given at a fixed order in $\alpha .$ Complex analysis is significantly used in the construction of the algorithm, we found a simpler way to calculate the involved integrals over contours in the complex planes than by any of the methods known at present.

Comments: 9 pages, Talk at ACAT 2019, Saas-Fee, Switzerland, revised version