Symbolic Expansion of Transcendental Functions

TL;DR

This paper introduces a C++ program that systematically expands certain transcendental functions, crucial for quantum field theory calculations, using Hopf algebra of nested sums.

Contribution

The paper presents a novel computer program leveraging Hopf algebra to automate the expansion of transcendental functions in quantum field theory.

Findings

The program efficiently performs expansions of transcendental functions.

It is implemented in C++ using the GiNaC library.

The approach is based on algebraic structures of nested sums.

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.