- XSummer - Transcendental Functions and Symbolic Summation in Form

TL;DR

This paper discusses algorithms implemented in Form for solving nested harmonic sums and their generalizations, which are crucial in evaluating higher-order corrections in quantum field theory.

Contribution

It introduces algebraic algorithms for symbolic summation of harmonic sums, enhancing computational tools for quantum field theory calculations.

Findings

Algorithms successfully solve nested sums

Implementation improves efficiency of perturbative calculations

Enhances capabilities of Form in symbolic summation

Abstract

Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their generalizations appear as building blocks, originating for example from the expansion of generalized hypergeometric functions around integer values of the parameters. In this Letter we discuss the implementation of several algorithms to solve these sums by algebraic means, using the computer algebra system Form.