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.

中文翻译：

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在DGLAP类型方程的运行耦合解中寻找所有阶的算法

摘要

我们提出了一种算法来找到一个解决DGLAP类型的积分微分方程在运行耦合的所有订单\（\阿尔法\）与在一个固定的顺序给出分裂功能\（\阿尔法\） 。复杂分析在算法的构造中大量使用，我们发现了一种比当前已知方法更简单的方法来计算复杂平面中轮廓上的所涉及积分。