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

## TL;DR

The paper introduces an algorithm that solves DGLAP-type equations across all orders in the running coupling, utilizing complex analysis for more efficient integral calculations.

## Contribution

It presents a novel algorithm that simplifies the calculation of solutions to DGLAP equations at all orders in the running coupling using complex analysis techniques.

## Key findings

- Developed a new algorithm for all-order solutions in the running coupling.
- Simplified the calculation of complex integrals over contours in the complex plane.
- Enhanced the efficiency of solving DGLAP-type equations.

## 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.