Computing Mellin representations and asymptotics of nested binomial sums in a symbolic way: the RICA package

TL;DR

The paper introduces the RICA software package designed to compute Mellin representations and asymptotic expansions of nested binomial sums, aiding in higher-order particle physics calculations and combinatorial mathematics.

Contribution

It provides a symbolic tool for deriving Mellin representations and asymptotics of nested binomial sums, facilitating analytic continuations in complex analysis and physics.

Findings

Successfully computes Mellin representations of nested sums

Generates asymptotic expansions at infinity

Aids in analytic continuation of sums in physics and mathematics

Abstract

Nested binomial sums form a particular class of sums that arise in the context of particle physics computations at higher orders in perturbation theory within QCD and QED, but that are also mathematically relevant, e.g., in combinatorics. We present the package RICA (Rule Induced Convolutions for Asymptotics), which aims at calculating Mellin representations and asymptotic expansions at infinity of those objects. These representations are of particular interest to perform analytic continuations of such sums.