Obtaining Bounds on The Sum of Divergent Series in Physics

TL;DR

This paper introduces a method to estimate bounds on the sum of divergent series in physics using a variational Borel map, demonstrated through multiple physical and mathematical examples.

Contribution

It presents a novel approach employing a variational Borel map to bound divergent series sums in physical contexts.

Findings

The method provides explicit bounds under certain conditions.

Application to various examples shows its versatility.

Demonstrates effectiveness in both physical and mathematical series.

Abstract

Under certain circumstances, some of which are made explicit here, one can deduce bounds on the full sum of a perturbation series of a physical quantity by using a variational Borel map on the partial series. The method is illustrated by applying it to various examples, physical and mathematical.