Numerical evaluation of two-dimensional harmonic polylogarithms

Abstract The two-dimensional harmonic polylogarithms G( a → (z);y), a generalization of the harmonic polylogarithms, themselves a generalization of Nielsen's polylogarithms, appear in analytic calculations of multi-loop radiative corrections in quantum field theory. We present an algorithm for the numerical evaluation of two-dimensional harmonic polylogarithms, with the two arguments y,z varying in th... Title of program: tdhpl version 1.0, release 1 Catalogue Id: ADPU_v1_0 Nature of problem Numerical evaluation of the two-dimensional harmonic polylogarithms up to weight 4 for real arguments restricted to 0 <= y <= 1, 0 <= z <= (1-y). These functions are emerging in Feynman graph integrals involving three mass scales. Versions of this program held in the CPC repository in Mendeley Data ADPU_v1_0; tdhpl version 1.0, release 1; 10.1016/S0010-4655(02)00139-X This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)**摘要** 二维调和多重对数函数（two-dimensional harmonic polylogarithms）$G(a o (z); y)$是调和多重对数函数（harmonic polylogarithms）的推广形式，而调和多重对数函数本身又是尼尔森多重对数函数（Nielsen's polylogarithms）的推广。这类函数出现在量子场论中多圈辐射修正的解析计算中。本文提出了一种用于数值计算二维调和多重对数函数的算法，其两个变量$y,z$的取值范围为…… 程序名称：tdhpl 版本1.0，发布版1 目录编号：ADPU_v1_0 **问题性质** 针对满足约束$0 leq y leq 1$、$0 leq z leq 1-y$的实变量，实现权重不超过4的二维调和多重对数函数的数值计算。这类函数在涉及三种质量标度的费曼图积分中逐渐得到应用。 存储于曼德雷数据（Mendeley Data）中的CPC库的该程序版本 ADPU_v1_0; tdhpl 版本1.0，发布版1; 10.1016/S0010-4655(02)00139-X 本程序源自贝尔法斯特女王大学所维护的CPC程序库（1969-2019）