A Symbolic Summation Approach to Find Optimal Nested Sum Representations

TL;DR

This paper introduces a symbolic summation framework to transform nested sums into minimal-depth representations, applicable to hypergeometric and related sums, with recent applications in quantum field theory.

Contribution

The paper presents a novel symbolic summation method for minimizing nested sum depth, extending to hypergeometric, q-hypergeometric, and mixed sums, with practical applications in physics.

Findings

Successfully minimizes nested sum depth in various sum classes

Applicable to hypergeometric, q-hypergeometric, and mixed sums

Demonstrated usefulness in quantum field theory computations

Abstract

We consider the following problem: Given a nested sum expression, find a sum representation such that the nested depth is minimal. We obtain a symbolic summation framework that solves this problem for sums defined, e.g., over hypergeometric, $q$-hypergeometric or mixed hypergeometric expressions. Recently, our methods have found applications in quantum field theory.