Symbolic expansion of transcendental functions

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018) Abstract Higher transcendental function occur frequently in the calculation of Feynman integrals in quantum field theory. Their expansion in a small parameter is a non-trivial task. We report on a computer program which allows the systematic expansion of certain classes of functions. The algorithms are based on the Hopf algebra of nested sums. The program is written in C++ and uses the GiNaC library. Title of program: nestedsums v 1.0 Catalogue Id: ADPX_v1_0 Nature of problem Systematic expansion of higher transcendental functions in a small parameter. These expansions occur, for example, in the calculation of loop integrals in quantum field theory within dimensional regularization. Versions of this program held in the CPC repository in Mendeley Data ADPX_v1_0; nestedsums v 1.0; 10.1016/S0010-4655(02)00261-8本程序源自贝尔法斯特女王大学馆藏的《计算机物理学报》（Computer Physics Communications，简称CPC）程序库（馆藏时段为1969-2018年）。 **摘要** 高等超越函数在量子场论的费曼积分（Feynman integrals）计算中频繁出现，对其进行小参数展开是一项非平凡的挑战性任务。本文介绍一款可对特定类别函数开展系统性展开的计算机程序，其算法基于嵌套和的霍普夫代数（Hopf algebra）。该程序采用C++语言编写，并依托GiNaC数学库实现相关功能。 **程序标题**：nestedsums v 1.0 **目录编号**：ADPX_v1_0 **问题范畴**： 本程序旨在实现高等超越函数的小参数系统性展开，此类展开常见于采用维度正规化（dimensional regularization）的量子场论圈积分计算场景中。 **Mendeley数据平台CPC资源库中存储的该程序版本**： ADPX_v1_0；nestedsums v 1.0；DOI: 10.1016/S0010-4655(02)00261-8