# Refined Holonomic Summation Algorithms in Particle Physics

## TL;DR

This paper introduces an advanced summation algorithm within difference rings to efficiently evaluate complex multi-sums in particle physics, supported by a new software package called RhoSum.

## Contribution

It presents a refined holonomic summation method and a software implementation that improves the handling of nested sums and products in difference ring frameworks.

## Key findings

- Enhanced ability to evaluate complicated multi-sums in particle physics
- Development of the RhoSum software package demonstrating the method
- Substantial improvement over previous summation techniques

## Abstract

An improved multi-summation approach is introduced and discussed that enables one to simultaneously handle indefinite nested sums and products in the setting of difference rings and holonomic sequences. Relevant mathematics is reviewed and the underlying advanced difference ring machinery is elaborated upon. The flexibility of this new toolbox contributed substantially to evaluating complicated multi-sums coming from particle physics. Illustrative examples of the functionality of the new software package RhoSum are given.